03206oam 2200565I 450 991015156640332120240501162423.01-315-35074-21-315-36774-210.1201/9781315367743 (CKB)3710000000941810(MiAaPQ)EBC4745246(OCoLC)966385775(BIP)70279797(BIP)54933649(EXLCZ)99371000000094181020180331h20172017 uy 0engurcnu||||||||rdacontentrdamediardacarrierIterative methods without inversion /Anatoly Galperin1st ed.Boca Raton, Fla. :CRC Press,[2017]©20171 online resource (241 pages) illustrationsMonographs and Research Notes in Mathematics1-4987-5892-4 1-4987-5896-7 Includes bibliographical references and index.1. Tools of the trade -- 2. Ulm's method -- 3. Ulm's method without derivatives -- 4. Broyden's method -- 5. Optimal secant updates of low rank -- 6. Optimal secant-type methods -- 7. Majorant generators and their convergence domains.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. Monographs and research notes in mathematics.Iterative methods (Mathematics)Numerical analysisBanach spacesHilbert spaceIterative methods (Mathematics)Numerical analysis.Banach spaces.Hilbert space.518/.26Galperin Anatoly993227FlBoTFGFlBoTFGBOOK9910151566403321Iterative methods without inversion2274293UNINA