Click Here to Download: https://ouo.io/5sTCz2 Iterative Methods without Inversion By: Anatoly Galperin Publisher: Chapman & Hall Print ISBN: 9781498758925, 1498758924 eText ISBN: 9781498758963, 1498758967 Copyright year: 2016 Format: PDF Available from $ 51.98 USD SKU 9781498758963R90 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 Ulmâs and Broydenâs methods. Convergence analyses of the methods considered are based on Kantorovichâs 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.
