LEADER 03614nam 22006375 450 001 9910146313703321 005 20210913161016.0 010 $a3-540-46518-9 024 7 $a10.1007/BFb0103927 035 $a(CKB)1000000000437287 035 $a(SSID)ssj0000322185 035 $a(PQKBManifestationID)11937857 035 $a(PQKBTitleCode)TC0000322185 035 $a(PQKBWorkID)10282526 035 $a(PQKB)10387504 035 $a(DE-He213)978-3-540-46518-8 035 $a(MiAaPQ)EBC5594575 035 $a(PPN)155222376 035 $a(EXLCZ)991000000000437287 100 $a20121227d2000 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aComputing the Zeros of Analytic Functions /$fby Peter Kravanja, Marc Van Barel 205 $a1st ed. 2000. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000. 215 $a1 online resource (VIII, 112 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1727 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-67162-5 327 $aZeros of analytic functions: Introduction -- Formal orthogonal polynomials -- An accurate algorithm to compute zeros of FOPs -- Numerical examples -- The software package ZEAL -- A derivative-free approach -- Clusters of zeros of analytic functions: How to abtain the centre of a cluster and its weight -- A numerical example -- Rational interpolation at roots of unity -- More numerical examples -- Zeros and ples of meromorphic functions: Introduction -- Theoretical considerations and numerical algorithm -- A numerical example -- Systems of analytic equations: Introduction -- A multidimensional logarithmic residue formula -- The algorithm -- Numerical examples. 330 $aComputing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1727 606 $aFunctions of complex variables 606 $aNumerical analysis 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aFunctions of complex variables. 615 0$aNumerical analysis. 615 14$aFunctions of a Complex Variable. 615 24$aNumerical Analysis. 676 $a515 686 $a65H05$2msc 686 $a30C15$2msc 686 $a65E05$2msc 700 $aKravanja$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut$065497 702 $aBarel$b Marc Van$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910146313703321 996 $aComputing the Zeros of Analytic Functions$92504503 997 $aUNINA