Iterative Methods without Inversion

1. Auflage 2016
ISBN: 978-1-4987-5892-5
Verlag: Taylor & Francis Inc

Buch, Englisch, 240 Seiten, Format (B × H): 243 mm x 164 mm, Gewicht: 472 g

Reihe: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Iterative Methods without Inversion presents the iterative methods for solving operator equations f(x) = 0 in Banach and/or Hilbert spaces. It covers methods that do not require inversions of f (or solving linearized subproblems). The typical representatives of the class of methods discussed are Ulm’s and Broyden’s methods. Convergence analyses of the methods considered are based on Kantorovich’s majorization principle which avoids unnecessary simplifying assumptions like differentiability of the operator or solvability of the equation. These analyses are carried out under a more general assumption about degree of continuity of the operator than traditional Lipschitz continuity: regular continuity.

Key Features

- The methods discussed are analyzed under the assumption of regular continuity of divided difference operator, which is more general and more flexible than the traditional Lipschitz continuity.

- An attention is given to criterions for comparison of merits of various methods and to the related concept of optimality of a method of certain class.

- Many publications on methods for solving nonlinear operator equations discuss methods that involve inversion of linearization of the operator, which task is highly problematic in infinite dimensions.

- Accessible for anyone with minimal exposure to nonlinear functional analysis.

Autoren/Hrsg.

Galperin, Anatoly

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Zahlensysteme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Introduction. Some useful tools of the trade. Ulm’s method. Ulm’s method without derivatives. Broyden’s method. Optimal secantupdates

of low rank. Optimal secant-type methods. Majorant generators and their convergence domains. Bibliography

Über Autor(innen)

Anatoly Galperin