03754nam 22007095 450 99646649310331620200703082117.03-642-30901-110.1007/978-3-642-30901-4(CKB)3400000000086161(SSID)ssj0000767536(PQKBManifestationID)11424062(PQKBTitleCode)TC0000767536(PQKBWorkID)10741671(PQKB)11732142(DE-He213)978-3-642-30901-4(MiAaPQ)EBC3070951(PPN)168317974(EXLCZ)99340000000008616120120913d2013 u| 0engurnn|008mamaatxtccrIterative Methods for Fixed Point Problems in Hilbert Spaces[electronic resource] /by Andrzej Cegielski1st ed. 2013.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2013.1 online resource (XVI, 298 p. 61 illus., 3 illus. in color.) Lecture Notes in Mathematics,0075-8434 ;2057Bibliographic Level Mode of Issuance: Monograph3-642-30900-3 Includes bibliographical references (p. 275-289) and index.1 Introduction -- 2 Algorithmic Operators -- 3 Convergence of Iterative Methods -- 4 Algorithmic Projection Operators -- 5 Projection methods.Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.Lecture Notes in Mathematics,0075-8434 ;2057Mathematical optimizationFunctional analysisCalculus of variationsNumerical analysisOperator theoryOptimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26008Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Calculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Mathematical optimization.Functional analysis.Calculus of variations.Numerical analysis.Operator theory.Optimization.Functional Analysis.Calculus of Variations and Optimal Control; Optimization.Numerical Analysis.Operator Theory.519.6Cegielski Andrzejauthttp://id.loc.gov/vocabulary/relators/aut477684BOOK996466493103316Iterative methods for fixed point problems in Hilbert spaces241162UNISA