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007 cr nn 008mamaa
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020 _a9783540465188
_9978-3-540-46518-8
024 7 _a10.1007/BFb0103927
_2doi
050 4 _aQA331-355
072 7 _aPBKD
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKD
_2thema
082 0 4 _a515.9
_223
100 1 _aKravanja, Peter.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aComputing the Zeros of Analytic Functions
_h[electronic resource] /
_cby Peter Kravanja, Marc Van Barel.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2000.
300 _aVIII, 112 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1727
505 0 _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.
520 _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.
650 0 _aFunctions of complex variables.
650 0 _aNumerical analysis.
650 1 4 _aFunctions of a Complex Variable.
_0http://scigraph.springernature.com/things/product-market-codes/M12074
650 2 4 _aNumerical Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M14050
700 1 _aBarel, Marc Van.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662180907
776 0 8 _iPrinted edition:
_z9783540671626
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1727
856 4 0 _uhttps://doi.org/10.1007/BFb0103927
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c10277
_d10277