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Argyros I. — Computational Theory of Iterative Methods
Argyros I. — Computational Theory of Iterative Methods

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Название: Computational Theory of Iterative Methods

Автор: Argyros I.

Аннотация:

The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 487

Добавлена в каталог: 18.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Additive operator      1
Antitone operator      19
Arnoldi's method      142
Autonomous differential equation      142
Banach lemma      4
Banach space      3
Banach space with convergence structure      342
Bijective linear operator      12
Bilinear operator      2
Biparametric family of multipoint iterations      231
Bounded linear operator      3
Chebyshev method      232
Chebyshev — Halley method      228
Conjugate gradient for the normal equations      438
Conjugate gradient solver      437
Continuation methods      300
Continuous linear operator      2
Contraction mapping      48
Convergence monitor      446
Convergence on a cone      316
Convergence on Lie groups      329
Convergence radius      141
Convex cone      17
Deformed method      213
Deuflhard — Heindl theorem      287
Differential of an operator      331
Dilation measure      298
Divided difference      20
Divided differences of order two      154
Dynamical system      297
Edelstein's Theorem      62
Energy norm      438
Equicontinuous operator      38
Error norm      438
Euler's method      307
Exponential map      330
Fibonacci sequence      185
Fixed point      47
Frechet derivative      6
Fredholm integral operator      50
Fredholm operator      11
Functional      2
G      44
Galerkin orthogonality      440
Gateaux derivative      27
Generalized minimum residual      438
Gershgorin's theorem      82
Halley method      232
Hausdorff topological space      414
Hemicontinuous operator      44
HLCP problem      356
Hoelder condition      104
Homogeneous operator      1
Identity operator      4
Inner inverse      242
Inner iteration      438
Inner product      11
Interior point method      353
Inverse function theorem      217
Inverse operator      4
Ishikawa iteration      70
Isotone operator      19
j-linear operators      2
Jacobi — Newton method      30
Jacobi-secant method      30
K-normed spaces      316
Kantorovich fixed point theorem      20
Krawczyk operator      288
Krylov subspace      440
Laplace operator      14
Laplace transform      10
LCP problem      353
Lie algebra      329
Lie bracket      329
Linear convergence mode      448
Linear space      1
Lipschitz condition      150
Logarithmic convexity      228
LP problem      353
Mean value theorem      9
Mesh independence      449
Mesh refinement      142
Midpoint method      228
Miranda theorem      291
Modified Newton — Kantorovich method      88
Monotone convergence      17
Moore theorem      287
Multipoint method      229
Neumann series      4
Newton Kantorovich theorem      89
Newton method      87
Newton SOR method      26
Newton — Kantorovich hypothesis      93
Newton — Kantorovich method      87
Newton — Leibniz formula      318
Newton — Mysovskikh condition      429
Nilpotent operator      5
Nonexpansive projector      256
Nonlinear operator      2
Nonstationary projection iteration      54
Norm of a linear operator      3
Normal equations      437
Normal map      254
Normal space      19
Outer inverse      242
Outer iteration      438
Partial Frechet Derivative      8
Partially ordered topological linear space      17
Peano's Theorem      307
Point to set-mapping      409
Point-based approximation      246
Pointwise ordering      18
Preconditioned conjugate gradient      438
Product of operators      12
Pseudocontraction      69
QP problem      353
Quadratic integral operator      93
Quasi method      387
Quasiconvex operator      56
Regular space      18
Relative error norm      441
Residual norm      438
Riccati operator      14
Riemannian integration      9
Secant method      117
Set of bilinear operators      2
Set of linear operators      2
Shadowing orbits      297
Spectral radius      316
Stability condition      452
Stationary projection iteration      54
Stirling's method      115
Strongly monotone operator      370
Strongly regular solution      379
Successive approximations      47
Successive substitutions      47
Super-Halley method      232
Symmetric operator      34
Tangent space      329
Taylor's theorem      10
Termination criterion      447
Trust regions      305
Two-point boundary value problem      347
Two-point Newton-like method      121
Two-step Newton method      26
Universal constant      204
Uryson operator      14
Variational inequality      393
Variational inequality problem      369
Vector algebra      11
Weak generalized Kantorovich condition      199
Weak Newton — Kantorovich hypothesis      132
Weierstrass theorem      50
Zero operator      11
Zincenko iteration      121
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