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1.

図書

図書
by Eugen Netto ; revised by the author ; and translated with his permission by F.N. Cole
出版情報: Ann Arbor : George Wahr, [189-?]  xi, 301 p. ; 23 cm
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2.

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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目次情報: 続きを見る
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:
3.

図書

図書
by Leonard Eugene Dickson
出版情報: New York : J. Wiley, 1922  vi, 168 p. ; 22 cm
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4.

図書

図書
by Florian Cajori
出版情報: New York ; London : Macmillan, 1904  ix, 239 p. ; 21 cm
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5.

図書

図書
by Samuel Marx Barton
出版情報: Boston : D.C. Heath & co., 1899  xii, 198 p ; 22 cm
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6.

図書

図書
written, translated, and revised by Jean-Pierre Tignol ; edited by T.S. Blyth
出版情報: Harlow, Essex, England : Longman Scientific & Technical , New York : Wiley, 1988  429 p. ; 24 cm
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7.

図書

図書
by Eugen Netto ; rev. by the author and translated with his permission by F.N. Cole
出版情報: Bronx, New York : Chelsea Pub. Co., [1964]  xi, 304 p. ; 21 cm
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