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1.

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図書
1. Approximation theory XVI : Nashville, TN, USA, May 19-22, 2019 (hbk.)
Gregory E. Fasshauer, Marian Neamtu, Larry L. Schumaker editors
出版情報: Cham : Springer, 2021  viii, 253 p. ; 25 cm
シリーズ名: Springer proceedings in mathematics & statistics ; 336
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2.

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図書
2. Metamodeling : a study of approximations in queueing models (: pbk)
Subhash Chandra Agrawal
出版情報: Cambridge, Mass. ; London : MIT Press, c1985  x, 262 p. ; 24 cm
シリーズ名: MIT Press series in computer systems
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目次情報: 続きを見る
Figures
Boxes
Tables
Series Foreword
Preface
Introduction / 1：
The Structure of the Modeling Process / 2：
Behavior Sequence Transformations and Models with Shadow Servers / 3：
State Space Transformations / 4：
Consistent Solution, Iteration, and Convergence / 5：
Conclusion / 6：
References
Appendixes
Comparison of Models of Preemptive Priority Systems / A：
The Aggregate Server Method for Multi-Class Networks / B：
Response Time Preservation Transformation / C：
Implications of Bistability in Preemptive Priority Systems / D：
Index
Figures
Boxes
Tables
3.

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図書
3. Asymptotic analysis (: us ; : gw)
J.D. Murray
出版情報: New York ; Tokyo : Springer-Verlag, c1984  vi, 164 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 48
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4.

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4. Linear approximation
by Arthur Sard
出版情報: Providence, R.I. : American Mathematical Society, 1963  xi, 544 p. ; 27 cm
シリーズ名: Mathematical surveys ; no. 9
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5.

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5. Approximation by polynomials with integral coefficients
Le Baron O. Ferguson
出版情報: Providence, R.I. : American Mathematical Society, 1980  xi, 160 p. ; 26 cm
シリーズ名: Mathematical surveys ; no. 17
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6.

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6. Difference methods and their extrapolations (: U.S. ; : Germany)
G.I. Marchuk, V.V. Shaidurov
出版情報: New York ; Tokyo : Springer-Verlag, c1983  x, 334 p. ; 25 cm
シリーズ名: Applications of mathematics ; 19
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7.

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図書
7. Lectures on complex approximation (: Boston ; : Basel)
Dieter Gaier ; translated by Renate McLaughlin
出版情報: Boston : Birkhäuser, c1987  ix, 196 p. ; 25 cm
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8.

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8. Stochastic approximation
M.T. Wasan
出版情報: London ; New York : Cambridge University Press, 1969  x, 202 p. ; 23 cm
シリーズ名: Cambridge tracts in mathematics and mathematical physics ; no. 58
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Preface
Introduction / 1：
The Robbins-Monro method / 2：
The Kiefer-Wolfowitz method / 3：
Applications / 4：
Multivariate stochastic-approximation methods / 5：
Asymptotic normality / 6：
The approximation for continuous random processes / 7：
Up-and-down method / 8：
Appendices
Bibliography
Index
Preface
Introduction / 1：
The Robbins-Monro method / 2：
9.

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図書
9. Semi-classical approximation in quantum mechanics
V.P. Maslov and M.V. Fedoriuk ; translated from the Russian by J. Niederle and J. Tolar
出版情報: Dordrecht, Holland ; Boston : D. Reidel Pub. Co. : sold and distributed in the U.S.A. and Canada by Kluwer Boston Inc., c1981  ix, 301 p. ; 23 cm
シリーズ名: Mathematical physics and applied mathematics ; v. 7
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10.

図書
図書
10. Generalized inverses of linear operators : representation and approximation
C. W. Groetsch
出版情報: New York : M. Dekker, c1977  viii, 165 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; . Series of monographs and textbook ; 37
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11.

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11. The approximate minimization of functionals
by James W. Daniel
出版情報: Englewood Cliffs, N.J. : Prentice-Hall, c1971  xi, 228 p ; 24 cm
シリーズ名: Prentice-Hall series in automatic computation
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12.

図書
図書
12. Approximation of functions of several variables and imbedding theorems (: gw ; : us)
S.M. Nikolʹskiĭ ; translated from the Russian by J.M. Danskin
出版情報: Berlin : New York : Springer-Verlag, 1975  viii, 420 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 205
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13.

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13. Analytic inequalities
D.S. Mitrinović ; in cooperation with P.M. Vasić
出版情報: Berlin ; New York : Springer-Verlag, 1970  xi, 400 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 165
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14.

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14. Best approximation in normed linear spaces by elements of linear subspaces
Ivan Singer ; [translated by Radu Georgescu]
出版情報: Bucharest : Pub. House of the Academy of the Socialist Republic of Romania , Berlin ; New York : Springer, 1970  415 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; Bd. 171
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15.

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15. Approximating integrals via Monte Carlo and deterministic methods
Michael Evans and Tim Swartz
出版情報: Oxford ; New York : Oxford University Press, c2000  ix, 288 p. ; 24 cm
シリーズ名: Oxford statistical science series ; 20
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16.

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図書
16. Joseph L. Walsh : selected papers (: hbk)
Theodore J. Rivlin, Edward B. Saff, editors
出版情報: New York : Springer, c2000  xliv, 682 p. ; 25 cm
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17.

図書
図書
17. Advances in multivariate approximation : proceedings of the 3rd International Conference on Multivariate Approximation Theory held at Witten-Bommerholz, Germany, September 27-October 2, 1998
edited by Werner Hauβmann, Kurt Jetter, Manfred Reimer
出版情報: Berlin : Wiley-VCH, c1999  334 p. ; 25 cm
シリーズ名: Mathematical research ; v. 107
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18.

図書
図書
18. A course in approximation theory (: hc)
Ward Cheney, Will Light
出版情報: Pacific Grove, Calif. ; Tokyo : Brooks/Cole, c2000  xiv, 357 p. ; 25 cm
シリーズ名: Brooks/Cole series in advanced mathematics
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19.

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図書
19. Constructive approximation on the sphere with applications to geomathematics
W. Freeden, T. Gervens, M. Schreiner
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 1998  xv, 427 p. ; 24 cm
シリーズ名: Numerical mathematics and scientific computation
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目次情報: 続きを見る
Notation / 1：
Polynomials / 2：
Scalar Spherical Harmonics / 3：
Green's Functions / 4：
Spherical Radial Basis Functions / 5：
Spherical Splines / 6：
Approximate Integration / 7：
Spherical Singular Integrals / 8：
Gabor and Toeplitz Transform / 9：
Continuous Wavelet Transform / 10：
Discrete Wavelet Transform / 11：
Vector Spherical Harmonics / 12：
Vectorial Approximation Methods / 13：
Tensor Spherical Harmonics / 14：
Tensorial Approximation Methods / 15：
References
Subject Index
Notation / 1：
Polynomials / 2：
Scalar Spherical Harmonics / 3：
20.

図書
図書
20. Lectures on proof verification and approximation algorithms
Ernst W. Mayr, Hans Jürgen Prömel, Angelika Steger (eds.)
出版情報: Berlin ; Tokyo : Springer, c1998  xii, 344 p. ; 24 cm
シリーズ名: Lecture notes in computer science ; 1367
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This textbook-like tutorial is a coherent
And essentially self-contained presentation of the enormous
Recent progress facilitated by the interplay
Between the theory of probabistically checkable
Proofs and aproximation algorithms
The basic concepts, methods, and results are presented
In a unified way to provide a smooth introduction for newcomers
These lectures are particularly useful for advanced
Courses or reading groups on the topic
This textbook-like tutorial is a coherent
And essentially self-contained presentation of the enormous
Recent progress facilitated by the interplay
21.

図書
図書
21. Approximate solutions of operator equations (alk. paper)
Mingjun Chen, Zhongying Chen, Guanrong Chen
出版情報: Singapore : World Scientific, c1997  xiii, 343 p. ; 23 cm
シリーズ名: Series in approximations and decompositions ; v. 9
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22.

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図書
22. Приближенное решение операторных уравнений
М.А. Красносельский ... [и др.]
出版情報: Москва : Наука, 1969  455 p. ; 23 cm
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23.

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図書
23. Fractional analysis : methods of motion decomposition
Igor V. Novozhilov
出版情報: Boston : Birkhäuser, 1997  x, 231 p. ; 25 cm
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24.

図書
図書
24. Spectral elements for transport-dominated equations
Daniele Funaro
出版情報: Berlin ; New York : Springer-Verlag, c1997  x, 211 p. ; 24 cm
シリーズ名: Lecture notes in computational science and engineering ; 1
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25.

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図書
25. Introduction to the theory of weighted polynomial approximation
by H.N. Mhaskar
出版情報: Singapore : World Scientific, c1996  xiv, 379 p. ; 23 cm
シリーズ名: Series in approximations and decompositions ; vol. 7
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26.

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図書
26. Harmonic approximation (: pbk)
Stephen J. Gardiner
出版情報: Cambridge : Cambridge University Press, 1995  xiii, 132 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 221
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27.

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27. Constructive approximation : advanced problems (: gw ; : us)
George G. Lorentz, Manfred v. Golitschek, Yuly Makovoz
出版情報: Berlin ; New York : Springer-Verlag, c1996  xi, 649 p. ; 24 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 304
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28.

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図書
28. Tractable reasoning in artificial intelligence
Marco Cadoli
出版情報: Berlin ; New York : Springer-Verlag, c1995  xiv, 247 p. ; 24 cm
シリーズ名: Lecture notes in computer science ; 941 . Lecture notes in artificial intelligence
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29.

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図書
29. A. Haar Memorial Conference (: set : North-Holland - v. 2 : Bolyai)
edited by J. Szabados and K. Tandori
出版情報: Amsterdam : North-Holland , Budapest : János Bolyai Mathematical Society , New York, N.Y. : Elsevier Science Publishing Company Inc., 1987  2 v. (1018 p.) ; 25 cm
シリーズ名: Colloquia Mathematica Societatis János Bolyai ; 49
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30.

図書
図書
30. Approximation of functions. 2nd ed. (: alk. paper)
by G.G. Lorentz
出版情報: New York, N.Y. : Chelsea Pub. Co., c1986  ix, 188 p. ; 24 cm
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目次情報: 続きを見る
Possibility of Approximation
Basic notions / 1：
Linear operators / 2：
Approximation theorems / 3：
The theorem of Stone / 4：
Notes / 5：
Polynomials of Best Approximation
Existence of polynomials of best approximation
Characterization of polynomials of best approximation
Applications of convexity
Chebyshev systems
Uniqueness of polynomials of best approximation
Chebyshev's theorem / 6：
Chebyshev polynomials / 7：
Approximation of some complex functions / 8：
Properties of Polynomials and Moduli of Continuity / 9：
Interpolation
Inequalities of Bernstein
The inequality of Markov
Growth of polynomials in the complex plane
Moduli of continuity
Moduli of smoothness
Classes of functions
The Degree of Approximation by Trigonometric Polynomials
Generalities
The theorem of Jackson
The degree of approximation of differentiable functions
Inverse theorems
Differentiable functions
The Degree of Approximation by Algebraic Polynomials
Preliminaries
The approximation theorems
Inequalities for the derivatives of polynomials
Approximation of analytic functions
Approximation by Rational Functions
Functions of Several Variables
Degree of rational approximation
Periodic functions of several variables
Approximation by algebraic polynomials
Approximation by Linear Polynomial Operators
Sums of de la Vallee-Poussin
Positive operators
The principle of uniform boundedness
Operators that preserve trigonometric polynomials
Trigonometric saturation classes
The saturation class of the Bernstein polynomials
Approximation of Classes of Functions
Introduction
Approximation in the space $L^1$
The degree of approximation of the classes $W^*_p$
Distance matrices
Approximation of the classes $\Lambda_{\omega}$
Arbitrary moduli of continuity; Approximation by operators
Analytic functions
Widths
Definitions and basic properties
Sets of continuous and differentiable functions
Widths of balls
Applications of theorem 2
Differential operators
Widths of the sets $\mathfrak{R}_l$
Entropy
Entropy and capacity
Entropy of classes of analytic functions
More general sets of analytic functions
Relations between entropy and widths
Representation of Functions of Several Variables by Functions of One Variable
The Theorem of Kolmogorov
The fundamental lemma
The completion of the proof
Functions not representable by superpositions
Bibliography
Index
Possibility of Approximation
Basic notions / 1：
Linear operators / 2：
31.

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31. Ordered cones and approximation (: gw ; : us)
Klaus Keimel, Walter Roth
出版情報: Berlin ; Tokyo : Springer-Verlag, c1992  vi, 134 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1517
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32.

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図書
32. The application of continued fractions and their generalizations to problems in approximation theory
by Alexey Nikolaevitch Khovanskii ; translated by Peter Wynn
出版情報: Groningen, Netherlands : P. Noordhoff, c1963  xii, 212 p. ; 23 cm
シリーズ名: Library of applied analysis and computational mathematics
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33.

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図書
33. Approximation theory : proceedings of the Sixth Southeastern Approximation Theorists Annual Conference
edited by George A. Anastassiou
出版情報: New York : M. Dekker, c1992  xxi, 524 p. ; 26 cm
シリーズ名: Lecture notes in pure and applied mathematics ; v. 138
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.. . Moment Problems and Their Applications to Characterization of Stochastic Processes, Queueing Theory, and Rounding Problems / George A. Anastassious ; S. T. Rachev Bivariate
Probabilistic Wavelet Approximation / Xiang Ming Yu
Sampling Designs for Estimating Integrals of Stochastic Processes Using Quadratic Mean Derivatives / Karim Benhenni ; Stamatis Cambanis
Para-Orthogonal Laurent Polynomials / Catherine M. Bonan-Hamada ; William B. Jones ; Arne Magnus
.. . Moment Problems and Their Applications to Characterization of Stochastic Processes, Queueing Theory, and Rounding Problems / George A. Anastassious ; S. T. Rachev Bivariate
Probabilistic Wavelet Approximation / Xiang Ming Yu
Sampling Designs for Estimating Integrals of Stochastic Processes Using Quadratic Mean Derivatives / Karim Benhenni ; Stamatis Cambanis
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34. Poisson approximation
A.D. Barbour, Lars Holst, Svante Janson
出版情報: Oxford [England] : Clarendon Press , New York : Oxford University Press, 1992  x, 277 p. ; 24 cm
シリーズ名: Oxford studies in probability ; 2
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目次情報: 続きを見る
Introduction
Upper bounds
Lower bounds
Random permutations
Random graphs
Occupancy and urn models
Spacings
Exceedances and extremes
Independent and dissociated terms
Poisson process approximation
Appendices
References
Index
Introduction
Upper bounds
Lower bounds
35.

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35. Theory of charge exchange
Robert A. Mapleton
出版情報: New York : Wiley-Interscience, c1972  x, 284 p ; 23 cm
シリーズ名: Wiley-Interscience series in atomic and molecular collisional processes
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36.

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36. Rational approximations and orthogonality
E.M. Nikishin, V.N. Sorokin ; [translated from the Russian by Ralph P. Boas ; translation edited by Sergei Gelfand]
出版情報: Providence, R.I. : American Mathematical Society, c1991  viii, 221 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 92
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Rational approximation of numbers
Pade approximants and orthogonal polynomials
Asymptotic properties of orthogonal polynomials
Simultaneous Pade approximants
Potential theory
Rational approximation of numbers
Pade approximants and orthogonal polynomials
Asymptotic properties of orthogonal polynomials
37.

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図書
37. Linear theory
by John Rischard Rice
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., c1964  x, 203 p. ; 24 cm
シリーズ名: Addison-Wesley series in computer science and information processing ; . The approximation of functions ; v. 1
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38.

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38. Progress in approximation theory
edited by Paul Nevai, Allan Pinkus
出版情報: Boston : Academic Press, c1991  xi, 916 p. ; 24 cm
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39.

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図書
39. Biorthogonality and its applications to numerical analysis
Claude Brezinski
出版情報: New York : M. Dekker, c1992  v, 166 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 156
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Introduction
Preliminaries Biorthogonality and Applications
Orthogonality for Polynomials Interpolation and Projection Kernel
The Interpolation Operator
The Method of Moments Lanczos' Method
The Bi-conjugate Gradient Method Fredholm Equation and PadT-Type
Approximants Adjacent Biorthogonal Families One-Step Forumlas Multistep Formulas
Applications Sequence Transformations Linear Multistep Methods
Approximation of Series Biorthogonal Polynomials Statistics and Least Squares
Introduction
Preliminaries Biorthogonality and Applications
Orthogonality for Polynomials Interpolation and Projection Kernel
40.

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図書
40. Topics in approximation theory (: U.S. ; : Germany)
[by] Harold S. Shapiro
出版情報: Berlin ; New York : Springer-Verlag, 1971  viii, 275 p ; 26 cm
シリーズ名: Lecture notes in mathematics ; 187
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41.

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41. Approximation of elliptic boundary-value problems
Jean-Pierre Aubin
出版情報: New York : Wiley-Interscience, c1972  xvii, 360 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 26
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目次情報: 続きを見る
Introduction
Aim and Scope / 1：
Neumann Problems / 2：
Introduction of Internal Approximations / 3：
Properties of Internal Approximations / 4：
Stability, Optimal Stability, and Regularity of the Convergence / 5：
The Case of Operators Mapping a Hilbert Space onto Its Dual / 6：
Finite-Element Approximations of Sobolev Spaces / 7：
Approximation of Nonhomogeneous Neumann Problems / 8：
Approximations of Nonhomogeneous Dirichlet Problems / 9：
A Posteriori Error Estimates / 10：
External and Partial Approximations / 11：
General Outline / 12：
Approximation of Solutions of Neumann Problems for Second-Order Linear Differential Equations
Weak Solutions of Neumann Problems for Second-Order Linear Differential Operators
The Neumann Boundary-Value Problem / 1-1：
Definition of Distributions / 1-2：
Weak Derivatives of a Distribution / 1-3：
Variational Formulation of the Problem / 1-4：
Weak Solutions of the Neumann Boundary-Value Problem / 1-5：
Sobolev Spaces / 1-6：
The Lax-Milgram Theorem / 1-7：
Approximation of an Abstract Variational Problem
The Galerkin Approximation of a Separable Hilbert Space / 2-1：
Approximation of a Hilbert Space / 2-2：
Internal Approximation of a Variational Equation / 2-3：
Existence, Uniqueness, and Convergence Properties / 2-4：
Estimates of Global Error / 2-5：
What Kind of Approximations Should Be Chosen? / 2-6：
Examples of Approximations of Sobolev Spaces
Piecewise-Linear Approximations of the Sobolev Space H[superscript 1] (I) / 3-1：
Estimates of Error Functions of Piecewise-Linear Approximations / 3-2：
Examples of Approximate Equations
Construction of a Finite-Difference Scheme / 4-1：
A Simpler Finite-Difference Scheme / 4-2：
Approximations of Hilbert Spaces
Hilbert Spaces and Their Duals
Dual of a Hilbert Space and Canonical Isometry
Example: Finite-Dimensional Hilbert Spaces
Hahn-Banach Theorem
Dual of a Dense Subspace
Imbedding of a Space into Its Dual
Example: Imbedding of Spaces of Functions into Spaces of Distributions
Dual of Closed Subspaces and Factor Spaces
Applications to Error Estimates / 1-8：
Dual of a Product / 1-9：
Dual of Domains of Operators / 1-10：
Examples: Dual of Sobolev Spaces H[subscript 0 superscript m](I) / 1-11：
Properties of Bounded Sets of Operators; Uniform Boundedness / 1-12：
Banach Theorem / 1-13：
Dual of Sobolev Spaces H[superscript m](I) / 1-14：
The Riesz-Fredholm Alternative / 1-15：
V-Elliptic and Coercive Operators / 1-16：
Quasi-Optimal Approximations
Stability Functions
Duality Relations between Error and Stability Functions
Estimates of the Stability Functions
Quasi-Optimal Approximations; Estimate of the Error Function
Truncation Errors and Error Functions
Optimal Approximations
Eigenvalues and Eigenvectors of Symmetric Compact Operators
Optimal Galerkin Approximations
Convergence and Optimality Properties / 3-3：
Spaces H[subscript Theta] / 3-4：
Optimal Restrictions and Prolongations; Applications
Optimal Restrictions and Prolongations
Dual Approximations
Construction of Optimal Prolongations and Restrictions / 4-3：
Miscellaneous Remarks / 4-4：
Characterization of Error and Stability Functions / 4-5：
Spaces of Order [Theta] / 4-6：
Approximation of Operators
Internal Approximations
Construction of an Internal Approximate Equation
The Case of Finite-Dimensional Discrete Spaces
The Case of Operators from V onto V[prime]
Stability of Internal Approximations of Operators
Convergence and Error Estimates
Approximation of a Sum of an Isomorphism and a Compact Operator
Approximation of Coercive and V-Elliptic Operators
Optimal and Quasi-Optimal Stability
Regularity of the Convergence and Estimates of Error in Terms of n-Width
Stability and Convergence in Smaller Spaces
Stability and Convergence in Larger Spaces
Approximation of the Value of a Functional at a Solution
Discrete Convergence, Consistency, and Optimal Approximation of Linear Operators
Discrete Convergence and Consistency
Optimal Approximation of Operators and Internal Approximations
Estimates of Error and Discrete Errors
Finite-Element Approximation of Functions of One Variable
Approximation of Functions of L[superscript 2] by Step Functions and by Convolution
The Space L[superscript 2] and the Discrete Space L[subscript h superscript 2]]
The Prolongations P[subscript h superscript 0]
The Restrictions r[subscript h]
The Theorem of Convergence
Convolution of Functions and Measures
Approximation by Convolution
Piecewise-Polynomial Approximations of Sobolev Spaces H[superscript m]
Finite-Difference Operators
Construction of Approximations of the Space H[superscript m]
Convergence Theorem
Explicit Form of Functions [Pi subscript m]
Properties of the Prolongations p[subscript h superscript m]
Optimal Properties of Prolongations p[subscript h superscript m] / 2-7：
Finite-Element Approximations of Sobolev Spaces H[superscript m]
Finite-Element Approximations
The Criterion of m-Convergence
Characterization of Convergent Finite-Element Approximations
Stability Properties of Finite-Element Approximations
Finite-Element Approximation of Functions of Several Variables
Approximations of the Sobolev Spaces H[superscript m](R[superscript n])
Notations
(2m + 1)[superscript n]-Level Piecewise-Polynomial Approximations
[2(2m)[superscript n] - (2m - 1)[superscript n]]-Level Piecewise-Polynomial Approximations
Approximations of the Sobolev Spaces H[superscript m]([Omega])
Sobolev Spaces H[superscript m]([Omega])
Finite-Element Approximations of H[superscript m]([Omega])
Quasi-Optimal Finite-Element Approximations of H[superscript m]([Omega])
Piecewise-Polynomial Approximations of H[superscript m]([Omega])
Approximation of the Sobolev Spaces H[subscript 0 superscript m]([Omega])
Sobolev Spaces H[subscript 0 superscript m]([Omega])
Finite-Element Approximations of H[subscript 0 superscript m]([Omega])
Convergent Finite-Element Approximations of H[subscript 0 superscript m]([Omega])
Boundary-Value Problems and the Trace Theorem
Some Variational Boundary-Value Problems for the Laplacian
The Laplacian
Characterization of Sobolev Spaces H[subscript 0 superscript 1]([Omega])
The Green Formula
The Dirichlet Problem for the Laplacian
The Neumann Problem for the Laplacian
A Mixed Problem for the Laplacian
An Oblique Problem for the Laplacian
Existence and Uniqueness of the Solutions
Variational Boundary-Value Problems and Their Adjoints
Spaces V, H and Operator [gamma]
Formal Operator [Lambda] Associated with a(u, v)
Abstract Neumann and Dirichlet Problems Associated with a(u, v)
Mixed Type Boundary-Value Problems Associated with a(u, v)
Existence and Uniqueness of the Solutions of Boundary-Value Problems
Formal Adjoint of an Operator and Green's Formula
Theorems of Regularity / 2-8：
The Trace Theorem and Properties of Sobolev Spaces
Statement of the Trace Theorem
Change of Coordinates
Sobolev Spaces H[superscript s](R[superscript n]) for Real Numbers s
Sobolev Spaces H[superscript s]([Gamma] and H[superscript s]([Omega])
Trace Operators and Operators of Extension: Theorems of Density / 3-5：
Properties of the Spaces H[superscript m](R[subscript + superscript n]) / 3-6：
Proof of the Trace Theorem / 3-7：
Sobolev Inequalities and the Trace Theorem in Space H[superscript s]([Omega]) / 3-8：
Theorem of Compactness / 3-9：
Examples of Boundary-Value Problems
Boundary-Value Problems for Second-Order Differential Operators
Second-Order Linear Differential Operators
Elliptic Second-Order Partial Differential Operators
The Dirichlet Problem
The Neumann Problem
Mixed Problems
Oblique Problems
Interface Problems
The Regularity Theorem
Theorems of Isomorphism
Value of the Solution at a Point of the Boundary
Problems with Elliptic Differential Boundary Conditions
Boundary-Value Problems for Differential Operators of Higher Order
Linear Differential Operators of Order 2k
Regularity and Theorems of Isomorphism
Other Boundary-Value Problems
Boundary Value Problems for [Delta][superscript 2] + [lambda]
Approximation of Neumann-Type Problems
Theorems of Convergence and Error Estimates
Internal Approximation of a Neumann-type Problem
Convergence and Estimates of Error in Larger Spaces
Approximation of Neumann Problems for Elliptic Operators of Order 2k
Approximation of Neumann Problems for Elliptic Differential Operators
Convergence Properties of Finite Element Approximations of Neumann Problems
The (2m + 1)[superscript n]-Level Approximations of the Neumann Problem
The [2(2m)[superscript n] - (2m - 1)[superscript n]]-Level Approximations of the Neumann Problem
Approximations of the Spaces H[superscript k]([Omega], [Lambda] and H([Omega], [Lambda]
Approximation of Other Neumann-Type Problems
Approximation of the Value of the Solution at a Point of the Boundary
Approximation of Oblique Boundary-Value Problems
Approximation of a Problem with Elliptic Boundary Conditions
Approximation of Interface Problems
Approximation of the Neumann Problem for [Delta][superscript 2] + [gamma]
Perturbed Approximations and Least-Squares Approximations
Perturbed Approximations
Internal Approximation of a Variational Boundary-Value Problem
Perturbed Approximation of a Variational Boundary-Value Problem
Convergence in the Initial Space
Estimates of Error
Convergence in Smaller Spaces
Convergence in Larger Spaces
Perturbed Approximations of Boundary-Value Problems
Perturbed Approximations by Finite-Element Approximations
Error Estimates and Regularity of the Convergence
The 3[superscript n]-level Perturbed Approximation of the Dirichlet Problem
Least-Squares Approximations
Least-Squares Approximation Schemes
Error Estimates (I)
Error Estimates (II)
Least-Squares Approximations of Dirichlet Problems
Conjugate Problems and A Posteriori Error Estimates
Conjugate Problems of Boundary-Value Problems
First Example of a Conjugate Problem
Second Example of a Conjugate Problem
Construction of Conjugate Problems
Applications to the Approximation of Dirichlet Problems
Approximation of the Dirichlet Problem (I)
Approximation of the Dirichlet Problem (II)
The Case of Second-Order Differential Operators
Finite-Element Approximations of the Spaces H[superscript k]([Omega], D*)
Spaces H[superscript k]([Omega], D*)
Approximations of the Space H[superscript k]([Omega], D*)
Approximation of the Second Example of a Conjugate Problem
Approximation of the Conjugate Dirichlet Problem
Properties of the Discrete Conjugate Problem
External Approximations; Stability, Convergence, and Error Estimates
Definition of External Approximations
Example: Partial Approximations of a Finite Intersection of Spaces
Stability and Convergence of External Approximations of Operators
Estimates of Error and Regularity of the Convergence
Properties of the External Error Functions
External and Partial Approximations of Variational Equations
Partial Approximation of a Split Variational Equation
External Approximation of Variational Equations
Partial Approximation of Neumann Problems
Perturbed Partial Approximation of Boundary-Value Problems
Partial Approximations of Sobolev Spaces
Spaces H([Omega], D[subscript i])
Partial Approximations of the Sobolev Space H[superscript 1]([Omega])
Estimates of Truncation Errors and External Error Functions
Partial Approximations of the Sobolev Spaces H[superscript m]([Omega]) and H[subscript 0 superscript m]([Omega])
Partial Approximation of Boundary-Value Problems
Partial Approximation of Second-Order Linear Operators
Partial Approximation of the Neumann Problem
Perturbed Partial Approximation of Mixed Boundary-Value Problems
Estimates of Error in the Interior
Partial Approximations of Higher-Order Differential Operators
Comments
References
Index
Introduction
Aim and Scope / 1：
Neumann Problems / 2：
42.

図書
図書
42. The principles and applications of variational methods
Martin Becker
出版情報: Cambridge, Mass. : M.I.T. Press, c1964  viii, 120 p. ; 25 cm
シリーズ名: Research monograph ; no. 27
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43.

図書
図書
43. Approximation theorems in commutative algebra : classical and categorical methods
by J. Alajbegović and J. Močkoř
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1992  xviii, 330 p. ; 25 cm
シリーズ名: Mathematics and its applications ; . East European series ; v. 59
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44.

図書
図書
44. Approximation and function spaces
editor of the volume, Zbigniew Ciesielski
出版情報: Warszawa : PWN-Polish Scientific Publishers, 1989  486 p. ; 25 cm
シリーズ名: Banach Center publications ; v. 22
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45.

図書
図書
45. Approximation theory and functional analysis
edited by Charles K. Chui
出版情報: Boston : Academic Press, c1991  x, 247 p. ; 24 cm
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目次情報: 続きを見る
Research and Survey Articles / H. Berens ; Y. Xu
On Bernstein-Durrineyer Polynomials with Jacob Weights / C. Chui
An Overview of Wavelets / G.A. Edgar ; L. Sucheston
A Note on Weak Inequalities in Orlicz and Lorentz Spaces / R.A. Lorentz
Bivariate Birkhoff Interpolation: A Survey / Y. Makovoz
Linear Approximations of Functions with Several Restricted Derivatives / K. Pan ; E.B. Saff
Some Characterizations Theorems for Measures Associated with Orthogonal Polynomials on the Unit Circle / S.D. Reimenschneider ; Z. Shen
Box Splines, Cardinal Series, and Wavelets / H. Rosenthal
Some Aspects of the Subspace Space Structure of Infinite Dimensional Banach Space / J. Roulier ; T. Rando ; B. Piper
Fairness and Monotone Curvature / N. Tomczak-Jacgermann
Projections on 2-Dimensional Spaces / R.S. Varga ; A. Ruttan
Real Versus Complex Best Rational Approximation
Research and Survey Articles / H. Berens ; Y. Xu
On Bernstein-Durrineyer Polynomials with Jacob Weights / C. Chui
An Overview of Wavelets / G.A. Edgar ; L. Sucheston
46.

図書
図書
46. Topological geometry
Ian R. Porteous
出版情報: London ; New York : Van Nostrand Reinhold, 1969  vii, 457 p. ; 24 cm
シリーズ名: The New university mathematics series
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47.

図書
図書
47. Approximate solution of operator equations
M. A. Krasnoselʹskii ... [et al.] ; translated by D. Louvish
出版情報: Groningen : Wolters-Noordhoff Pub., c1972  xii, 484 p. ; 23 cm
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48.

図書
図書
48. Polynomial approximation
[by] Robert P. Feinerman [and] Donald J. Newman
出版情報: Baltimore : Williams & Wilkins, c1974  viii, 148 p. ; 24 cm
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49.

図書
図書
49. One-dimensional theory
Paul L. Butzer, Rolf J. Nessel
出版情報: Basel ; Stuttgart : Birkhäuser, 1971  xvi, 553 p. ; 25 cm
シリーズ名: Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften ; . Mathematische Reihe ; Bd. 40 . Fourier analysis and approximation ; v. 1
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50.

図書
図書
50. Optimization and approximation
W. Krabs
出版情報: Chichester, [Eng.] ; New York : Wiley, c1979  xii, 220 p. ; 24 cm
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