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1.

図書

図書
Hugh G. Campbell
出版情報: New York : Appleton-Century-Crofts, c1971  xiii, 336, A39 p. ; 24 cm
シリーズ名: The Appleton-Century mathematics series
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2.

図書

図書
Richard S. Varga
出版情報: Berlin : Springer, c2004  x, 226 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 36
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Preface / I:
Basic Theory / 1:
Geršgorin's Theorem / 1.1:
Extensions of Geršgorin's Theorem via Graph Theory / 1.2:
Analysis Extensions of Geršgorin's Theorem and Fan's Theorem / 1.3:
A Norm Derivation of Geršgorin's Theorem 1.1 / 1.4:
Geršgorin-Type Eigenvalue Inclusion Theorems / 2:
Brauer's Ovals of Cassini / 2.1:
Higher-Order Lemniscates / 2.2:
Comparison of the Brauer Sets and the Brualdi Sets / 2.3:
The Sharpness of Brualdi Lemniscate Sets / 2.4:
An Example / 2.5:
More Eigenvalue Inclusion Results / 3:
The Parodi-Schneider Eigenvalue Inclusion Sets / 3.1:
The Field of Values of a Matrix / 3.2:
Newer Eigenvalue Inclusion Sets / 3.3:
The Pupkov-Solov'ev Eigenvalue Inclusions Set / 3.4:
Minimal Geršgorin Sets and Their Sharpness / 4:
Minimal Geršgorin Sets / 4.1:
Minimal Geršgorin Sets via Permutations / 4.2:
A Comparison of Minimal Geršgorin Sets and Brualdi Sets / 4.3:
G-Functions / 5:
The Sets <$>{\cal F}_{\bf n}<$> and <$>{\cal G}_{\bf n}<$> / 5.1:
Structural Properties of <$>{\cal G}_{\bf n}<$> and <$>{\cal G}_{\bf n}^{\bf c}<$> / 5.2:
Minimal G-Functions / 5.3:
Minimal G-Functions with Small Domains of Dependence / 5.4:
Connections with Brauer Sets and Generalized Brualdi Sets / 5.5:
Geršgorin-Type Theorems for Partitioned Matrices / 6:
Partitioned Matrices and Block Diagonal Dominance / 6.1:
A Different Norm Approach / 6.2:
A Variation on a Theme by Brualdi / 6.3:
G-Functions in the Partitioned Case / 6.4:
Geršgorin's Paper from 1931, and Comments / Appendix A:
Vector Norms and Induced Operator Norms / Appendix B:
The Perron-Frobenius Theory of Nonnegative Matrices / Appendix C:
Matlab 6 Programs / Appendix D:
References
Preface / I:
Basic Theory / 1:
Geršgorin's Theorem / 1.1:
3.

図書

図書
James J. Callahan
出版情報: New York : Springer, c2000  xvi, 451 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
Arbitrary frames
Surfaces and curvatures
Intrinsic geometry
General relativity
Consequences
Relativity before 1905
Special relativityùkinematics
Special relativityùkinetics
4.

図書

図書
Paul C. Shields
出版情報: Reading, Mass. : Addison-Wesley Pub. Co., c1964  xii, 288 p. ; 24 cm
シリーズ名: Addison-Wesley series in mathematics / Eric Reissner, consulting editor
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5.

図書

図書
Władysław Ślebodziński
出版情報: Warszawa : Państwowe Wydawnictwo Naukowe, 1954-1963  2 v. ; 25 cm
シリーズ名: Monografie matematyczne ; t. 31, 40
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6.

図書

図書
Michael W. Frazier
出版情報: New York ; Tokyo : Springer, c1999  xvi, 501 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
Background: Complex Numbers and Linear Algebra / 1:
Real Numbers and Complex Numbers / 1.1:
Complex Series, Euler's Formula, and the Roots of Unity / 1.2:
Vector Spaces and Bases / 1.3:
Linear Transformations, Matrices, and Change of Basis / 1.4:
Diagonalization of Linear Transformations and Matrices / 1.5:
Inner Products, Orthonormal Bases, and Unitary Matrices / 1.6:
The Discrete Fourier Transform / 2:
Basic Properties of the Discrete Fourier Transform / 2.1:
Translation-Invariant Linear Transformations / 2.2:
The Fast Fourier Transform / 2.3:
Wavelets on $bZ_N$ / 3:
Construction of Wavelets on $bZ_N$: The First Stage / 3.1:
Construction of Wavelets on $bZ_N$: The Iteration Step / 3.2:
Examples and Applications / 3.3:
Wavelets on $bZ$ / 4:
$ ell ^2(bZ)$ / 4.1:
Complete Orthonormal Sets in Hilbert Spaces / 4.2:
$L^2([- pi , pi ))$ and Fourier Series / 4.3:
The Fourier Transform and Convolution on $ ell ^2(bZ)$ / 4.4:
First-Stage Wavelets on $bZ$ / 4.5:
The Iteration Step for Wavelets on $bZ$ / 4.6:
Implementation and Examples / 4.7:
Wavelets on $bR$ / 5:
$L^2(bR)$ and Approximate Identities / 5.1:
The Fourier Transform on $bR$ / 5.2:
Multiresolution Analysis and Wavelets / 5.3:
Construction of Multiresolution Analyses / 5.4:
Wavelets with Compact Support and Their Computation / 5.5:
Wavelets and Differential Equations / 6:
The Condition Number of a Matrix / 6.1:
Finite Difference Methods for Differential Equations / 6.2:
Wavelet-Galerkin Methods for Differential Equations / 6.3:
Bibliography
Index
Preface
Acknowledgments
Prologue: Compression of the FBI Fingerprint Files
7.

図書

図書
by L.E. Dickson
出版情報: Cambridge : University Press, 1914  viii, 73 p. ; 22 cm
シリーズ名: Cambridge tracts in mathematics ; no. 16
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8.

図書

図書
par J. Larrieu
出版情報: Paris : Dunod, 1965  168, [1] p ; 24 cm
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9.

図書

図書
Morris W. Hirsch, Stephen Smale, Robert L. Devaney
出版情報: San Diego ; Tokyo : Elsevier Academic Press, c2004  xiv, 417 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 60
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Preface
First-Order Equations / Chapter 1:
The Simplest Example / 1.1:
The Logistic Population Model / 1.2:
Constant Harvesting and Bifurcations / 1.3:
Periodic Harvesting and Periodic Solutions / 1.4:
Computing the Poincare Map / 1.5:
Exploration: A Two-Parameter Family / 1.6:
Planar Linear Systems / Chapter 2:
Second-Order Differential Equations / 2.1:
Planar Systems / 2.2:
Preliminaries from Algebra / 2.3:
Eigenvalues and Eigenvectors / 2.4:
Solving Linear Systems / 2.6:
The Linearity Principle / 2.7:
Phase Portraits for Planar Systems / Chapter 3:
Real Distinct Eigenvalues / 3.1:
Complex Eigenvalues / 3.2:
Repeated Eigenvalues / 3.3:
Changing Coordinates / 3.4:
Classification of Planar Systems / Chapter 4:
The Trace-Determinant Plane / 4.1:
Dynamical Classification / 4.2:
Exploration: A 3D Parameter Space / 4.3:
Higher Dimensional Linear Algebra / Chapter 5:
Preliminaries from Linear Algebra / 5.1:
Bases and Subspaces / 5.2:
Genericity / 5.5:
Higher Dimensional Linear Systems / Chapter 6:
Distinct Eigenvalues / 6.1:
Harmonic Oscillators / 6.2:
The Exponential of a Matrix / 6.3:
Nonautonomous Linear Systems / 6.5:
Nonlinear Systems / Chapter 7:
Dynamical Systems / 7.1:
The Existence and Uniqueness Theorem / 7.2:
Continuous Dependence of Solutions / 7.3:
The Variational Equation / 7.4:
Exploration: Numerical Methods / 7.5:
Equilibria in Nonlinear Systems / Chapter 8:
Some Illustrative Examples / 8.1:
Nonlinear Sinks and Sources / 8.2:
Saddles / 8.3:
Stability / 8.4:
Bifurcations / 8.5:
Exploration: Complex Vector Fields / 8.6:
Global Nonlinear Techniques / Chapter 9:
Nullclines / 9.1:
Stability of Equilibria / 9.2:
Gradient Systems / 9.3:
Hamiltonian Systems / 9.4:
Exploration: The Pendulum with Constant Forcing / 9.5:
Closed Orbits and Limit Sets / Chapter 10:
Limit Sets / 10.1:
Local Sections and Flow Boxes / 10.2:
The Poincare Map / 10.3:
Monotone Sequences in Planar Dynamical Systems / 10.4:
The Poincare-Bendixson Theorem / 10.5:
Applications of Poincare-Bendixson / 10.6:
Exploration: Chemical Reactions That Oscillate / 10.7:
Applications in Biology / Chapter 11:
Infectious Diseases / 11.1:
Predator/Prey Systems / 11.2:
Competitive Species / 11.3:
Exploration: Competition and Harvesting / 11.4:
Applications in Circuit Theory / Chapter 12:
An RLC Circuit / 12.1:
The Lienard Equation / 12.2:
The van der Pol Equation / 12.3:
A Hopf Bifurcation / 12.4:
Exploration: Neurodynamics / 12.5:
Applications in Mechanics / Chapter 13:
Newton's Second Law / 13.1:
Conservative Systems / 13.2:
Central Force Fields / 13.3:
The Newtonian Central Force System / 13.4:
Kepler's First Law / 13.5:
The Two-Body Problem / 13.6:
Blowing Up the Singularity / 13.7:
Exploration: Other Central Force Problems / 13.8:
Exploration: Classical Limits of Quantum Mechanical Systems / 13.9:
The Lorenz System / Chapter 14:
Introduction to the Lorenz System / 14.1:
Elementary Properties of the Lorenz System / 14.2:
The Lorenz Attractor / 14.3:
A Model for the Lorenz Attractor / 14.4:
The Chaotic Attractor / 14.5:
Exploration: The Rossler Attractor / 14.6:
Discrete Dynamical Systems / Chapter 15:
Introduction to Discrete Dynamical Systems / 15.1:
The Discrete Logistic Model / 15.2:
Chaos / 15.4:
Symbolic Dynamics / 15.5:
The Shift Map / 15.6:
The Cantor Middle-Thirds Set / 15.7:
Exploration: Cubic Chaos / 15.8:
Exploration: The Orbit Diagram / 15.9:
Homoclinic Phenomena / Chapter 16:
The Shil'nikov System / 16.1:
The Horseshoe Map / 16.2:
The Double Scroll Attractor / 16.3:
Homoclinic Bifurcations / 16.4:
Exploration: The Chua Circuit / 16.5:
Existence and Uniqueness Revisited / Chapter 17:
Proof of Existence and Uniqueness / 17.1:
Continuous Dependence on Initial Conditions / 17.3:
Extending Solutions / 17.4:
Nonautonomous Systems / 17.5:
Differentiability of the Flow / 17.6:
Bibliography
Index
Preface
First-Order Equations / Chapter 1:
The Simplest Example / 1.1:
10.

図書

図書
Peter Deuflhard
出版情報: Berlin ; Tokyo : Springer, c2004  xii, 424 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; 35
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Outline of Contents
Introduction / 1:
Newton-Raphson Method for Scalar Equations / 1.1:
Newton's Method for General Nonlinear Problems / 1.2:
Classical convergence theorems revisited / 1.2.1:
Affine invariance and Lipschitz conditions / 1.2.2:
The algorithmic paradigm / 1.2.3:
A Roadmap of Newton-type Methods / 1.3:
Adaptive Inner Solvers for Inexact Newton Methods / 1.4:
Residual norm minimization: GMRES / 1.4.1:
Energy norm minimization: PCG / 1.4.2:
Error norm minimization: CGNE / 1.4.3:
Error norm reduction: GBIT / 1.4.4:
Linear multigrid methods / 1.4.5:
Exercises
Algebraic Equations / Part I:
Systems of Equations: Local Newton Methods / 2:
Error Oriented Algorithms / 2.1:
Ordinary Newton method / 2.1.1:
Simplified Newton method / 2.1.2:
Newton-like methods / 2.1.3:
Broyden's 'good' rank-1 updates / 2.1.4:
Inexact Newton-ERR methods / 2.1.5:
Residual Based Algorithms / 2.2:
Broyden's 'bad' rank-1 updates / 2.2.1:
Inexact Newton-RES method / 2.2.4:
Convex Optimization / 2.3:
Inexact Newton-PCG method / 2.3.1:
Systems of Equations: Global Newton Methods / 3:
Globalization Concepts / 3.1:
Componentwise convex mappings / 3.1.1:
Steepest descent methods / 3.1.2:
Trust region concepts / 3.1.3:
Newton path / 3.1.4:
Residual Based Descent / 3.2:
Affine contravariant convergence analysis / 3.2.1:
Adaptive trust region strategies / 3.2.2:
Error Oriented Descent / 3.2.3:
General level functions / 3.3.1:
Natural level function / 3.3.2:
Convex Functional Descent / 3.3.3:
Affine conjugate convergence analysis / 3.4.1:
Least Squares Problems: Gauss-Newton Methods / 3.4.2:
Linear Least Squares Problems / 4.1:
Unconstrained problems / 4.1.1:
Equality constrained problems / 4.1.2:
Local Gauss-Newton methods / 4.2:
Global Gauss-Newton methods / 4.2.2:
Adaptive trust region strategy / 4.2.3:
Local convergence results / 4.3:
Local Gauss-Newton algorithms / 4.3.2:
Global convergence results / 4.3.3:
Adaptive rank strategies / 4.3.4:
Underdetermined Systems of Equations / 4.4:
Local quasi-Gauss-Newton method / 4.4.1:
Global Gauss-Newton method / 4.4.2:
Parameter Dependent Systems: Continuation Methods / 5:
Newton Continuation Methods / 5.1:
Classification of continuation methods / 5.1.1:
Affine covariant feasible stepsizes / 5.1.2:
Adaptive pathfollowing algorithms / 5.1.3:
Gauss-Newton Continuation Method / 5.2:
Discrete tangent continuation beyond turning points / 5.2.1:
Adaptive stepsize control / 5.2.2:
Computation of Simple Bifurcations / 5.3:
Augmented systems for critical points / 5.3.1:
Newton-like algorithm for simple bifurcations / 5.3.2:
Branching-off algorithm / 5.3.3:
Differential Equations / Part II:
Stiff ODE Initial Value Problems / 6:
Affine Similar Linear Contractivity / 6.1:
Nonstiff versus Stiff Initial Value Problems / 6.2:
Picard iteration versus Newton iteration / 6.2.1:
Newton-type uniqueness theorems / 6.2.2:
Uniqueness Theorems for Implicit One-step Methods / 6.3:
Pseudo-transient Continuation for Steady State Problems / 6.4:
Exact pseudo-transient continuation / 6.4.1:
Inexact pseudo-transient continuation / 6.4.2:
ODE Boundary Value Problems / 7:
Multiple Shooting for Timelike BVPs / 7.1:
Cyclic linear systems / 7.1.1:
Realization of Newton methods / 7.1.2:
Realization of continuation methods / 7.1.3:
Parameter Identification in ODEs / 7.2:
Periodic Orbit Computation / 7.3:
Single orbit computation / 7.3.1:
Orbit continuation methods / 7.3.2:
Fourier collocation method / 7.3.3:
Polynomial Collocation for Spacelike BVPs / 7.4:
Discrete versus continuous solutions / 7.4.1:
Quasilinearization as inexact Newton method / 7.4.2:
PDE Boundary Value Problems / 8:
Asymptotic Mesh Independence / 8.1:
Global Discrete Newton Methods / 8.2:
General PDEs / 8.2.1:
Elliptic PDEs / 8.2.2:
Inexact Newton Multilevel FEM for Elliptic PDEs / 8.3:
Local Newton-Galerkin methods / 8.3.1:
Global Newton-Galerkin methods / 8.3.2:
References
Software
Index
Outline of Contents
Introduction / 1:
Newton-Raphson Method for Scalar Equations / 1.1:
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