LEADER 03602nam 2200649 450 001 996466632403316 005 20220304174325.0 010 $a3-540-48174-5 024 7 $a10.1007/BFb0083599 035 $a(CKB)1000000000437419 035 $a(SSID)ssj0000324206 035 $a(PQKBManifestationID)12072484 035 $a(PQKBTitleCode)TC0000324206 035 $a(PQKBWorkID)10322713 035 $a(PQKB)10218044 035 $a(DE-He213)978-3-540-48174-4 035 $a(MiAaPQ)EBC5579726 035 $a(Au-PeEL)EBL5579726 035 $a(OCoLC)1066184886 035 $a(MiAaPQ)EBC6842537 035 $a(Au-PeEL)EBL6842537 035 $a(OCoLC)793079167 035 $a(PPN)155225731 035 $a(EXLCZ)991000000000437419 100 $a20220304d1989 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIterative methods for simultaneous inclusion of polynomial zeros /$fMiodrag Petkovic? 205 $a1st ed. 1989. 210 1$aBerlin, Heidelberg :$cSpringer-Verlag,$d[1989] 210 4$dİ1989 215 $a1 online resource (XII, 268 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1387 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-387-51485-6 311 $a3-540-51485-6 327 $aBasic concepts -- Iterative methods without derivatives -- Generalized root iterations -- Bell's polynomials and parallel disk iterations -- Computational efficiency of simultaneous methods. 330 $aThe simultaneous inclusion of polynomial complex zeros is a crucial problem in numerical analysis. Rapidly converging algorithms are presented in these notes, including convergence analysis in terms of circular regions, and in complex arithmetic. Parallel circular iterations, where the approximations to the zeros have the form of circular regions containing these zeros, are efficient because they also provide error estimates. There are at present no book publications on this topic and one of the aims of this book is to collect most of the algorithms produced in the last 15 years. To decrease the high computational cost of interval methods, several effective iterative processes for the simultaneous inclusion of polynomial zeros which combine the efficiency of ordinary floating-point arithmetic with the accuracy control that may be obtained by the interval methods, are set down, and their computational efficiency is described. The rate of these methods is of interest in designing a package for the simultaneous approximation of polynomial zeros, where automatic procedure selection is desired. The book is both a text and a reference source for mathematicans, engineers, physicists and computer scientists who are interested in new developments and applications, but the material is also accessible to anyone with graduate level mathematical background and some knowledge of basic computational complex analysis and programming. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1387 606 $aIterative methods (Mathematics) 606 $aPolynomials 606 $aInterval analysis (Mathematics) 615 0$aIterative methods (Mathematics) 615 0$aPolynomials. 615 0$aInterval analysis (Mathematics) 676 $a511.42 700 $aPetkovic?$b Miodrag$058168 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466632403316 996 $aIterative methods for simultaneous inclusion of polynomial zeros$978586 997 $aUNISA