LEADER 04147nam 22006015 450 001 9910254098403321 005 20220404180514.0 010 $a3-319-33255-4 024 7 $a10.1007/978-3-319-33255-0 035 $a(CKB)3710000000734709 035 $a(EBL)4573806 035 $a(DE-He213)978-3-319-33255-0 035 $a(MiAaPQ)EBC4573806 035 $a(PPN)194379191 035 $a(EXLCZ)993710000000734709 100 $a20160630d2016 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aApproximate solutions of common fixed-point problems /$fby Alexander J. Zaslavski 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (457 p.) 225 1 $aSpringer Optimization and Its Applications,$x1931-6828 ;$v112 300 $aDescription based upon print version of record. 311 $a3-319-33253-8 320 $aIncludes bibliographical references and index. 327 $a1.Introduction -- 2. Dynamic string-averaging methods in Hilbert spaces -- 3. Iterative methods in metric spaces -- 4. Dynamic string-averaging methods in normed spaces -- 5. Dynamic string-maximum methods in metric spaces -- 6. Spaces with generalized distances -- 7. Abstract version of CARP algorithm -- 8. Proximal point algorithm -- 9. Dynamic string-averaging proximal point algorithm -- 10. Convex feasibility problems -- 11. Iterative subgradient projection algorithm -- 12. Dynamic string-averaging subgradient projection algorithm.? References.? Index. . 330 $aThis book presents results on the convergence behavior of algorithms which are known as vital tools for solving convex feasibility problems and common fixed point problems. The main goal for us in dealing with a known computational error is to find what approximate solution can be obtained and how many iterates one needs to find it. According to know results, these algorithms should converge to a solution. In this exposition, these algorithms are studied, taking into account computational errors which remain consistent in practice. In this case the convergence to a solution does not take place. We show that our algorithms generate a good approximate solution if computational errors are bounded from above by a small positive constant. Beginning with an introduction, this monograph moves on to study: · dynamic string-averaging methods for common fixed point problems in a Hilbert space · dynamic string methods for common fixed point problems in a metric space · dynamic string-averaging version of the proximal algorithm · common fixed point problems in metric spaces · common fixed point problems in the spaces with distances of the Bregman type · a proximal algorithm for finding a common zero of a family of maximal monotone operators · subgradient projections algorithms for convex feasibility problems in Hilbert spaces . 410 0$aSpringer Optimization and Its Applications,$x1931-6828 ;$v112 606 $aCalculus of variations 606 $aNumerical analysis 606 $aOperator theory 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 615 0$aCalculus of variations. 615 0$aNumerical analysis. 615 0$aOperator theory. 615 14$aCalculus of Variations and Optimal Control; Optimization. 615 24$aNumerical Analysis. 615 24$aOperator Theory. 676 $a510 700 $aZaslavski$b Alexander J$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721713 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254098403321 996 $aApproximate solutions of common fixed-point problems$91523163 997 $aUNINA