03012nam 22006255 450 991014631490332120200702155852.03-540-45592-210.1007/BFb0103934(CKB)1000000000437281(SSID)ssj0000321562(PQKBManifestationID)12115902(PQKBTitleCode)TC0000321562(PQKBWorkID)10280881(PQKB)10719241(DE-He213)978-3-540-45592-9(MiAaPQ)EBC6306503(MiAaPQ)EBC5585147(Au-PeEL)EBL5585147(OCoLC)1066179021(PPN)155197746(EXLCZ)99100000000043728120121227d2000 u| 0engurnn|008mamaatxtccrAverage-Case Analysis of Numerical Problems /by Klaus Ritter1st ed. 2000.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2000.1 online resource (XI, 252 p.) Lecture Notes in Mathematics,0075-8434 ;1733Bibliographic Level Mode of Issuance: Monograph3-540-67449-7 Linear problems: Definitions and a classical example -- Second-order results for linear problems -- Integration and approximation of univariate functions -- Linear problems for univariate functions with noisy data -- Integration and approximation of multivariate functions -- Nonlinear methods for linear problems -- Nonlinear problems.The average-case analysis of numerical problems is the counterpart of the more traditional worst-case approach. The analysis of average error and cost leads to new insight on numerical problems as well as to new algorithms. The book provides a survey of results that were mainly obtained during the last 10 years and also contains new results. The problems under consideration include approximation/optimal recovery and numerical integration of univariate and multivariate functions as well as zero-finding and global optimization. Background material, e.g. on reproducing kernel Hilbert spaces and random fields, is provided.Lecture Notes in Mathematics,0075-8434 ;1733Numerical analysisStatistics Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Statistics, generalhttps://scigraph.springernature.com/ontologies/product-market-codes/S0000XNumerical analysis.Statistics .Numerical Analysis.Statistics, general.519.4Ritter Klausauthttp://id.loc.gov/vocabulary/relators/aut62632MiAaPQMiAaPQMiAaPQBOOK9910146314903321Average-case analysis of numerical problems374165UNINA