Iterative Methods Without Inversion

ISBN-13: 9781498758925 / Angielski / Twarda / 2016 / 230 str.

Anatoly Galperin

Opis

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.

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O autorze

Anatoly Galperin