LEADER 04163nam 22006495 450 001 9910739414203321 005 20200629210304.0 010 $a1-4614-8453-7 024 7 $a10.1007/978-1-4614-8453-0 035 $a(CKB)3710000000078710 035 $a(SSID)ssj0001090867 035 $a(PQKBManifestationID)11686825 035 $a(PQKBTitleCode)TC0001090867 035 $a(PQKBWorkID)11021087 035 $a(PQKB)11612342 035 $a(DE-He213)978-1-4614-8453-0 035 $a(MiAaPQ)EBC6311933 035 $a(MiAaPQ)EBC1591826 035 $a(Au-PeEL)EBL1591826 035 $a(CaPaEBR)ebr10968979 035 $a(OCoLC)869010295 035 $a(PPN)176098836 035 $a(EXLCZ)993710000000078710 100 $a20131206d2013 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 12$aA Graduate Introduction to Numerical Methods $eFrom the Viewpoint of Backward Error Analysis /$fby Robert M. Corless, Nicolas Fillion 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (XXXIX, 869 p. 194 illus., 10 illus. in color.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4614-8452-9 327 $aComputer Arithmetic & Fundamental Concepts of Computation -- Polynomials and Series -- Rootfinding and Function Evaluation -- Solving Ax = b -- Solving Ax =l x -- Structured Linear Systems.-Iterative Methods -- Polynomial and Rational Interpolation -- The Discrete Fourier Transform -- Numerical Integration -- Numerical Differentiation and Finite Differences -- Numerical Solution of ODEs -- Numerical Methods for ODEs -- Numerical Solutions of Boundary Value Problems -- Numerical Solution of Delay DEs -- Numerical Solution of PDEs. 330 $aThis book provides an extensive introduction to numerical computing from the viewpoint of backward error analysis. The intended audience includes students and researchers in science, engineering and mathematics. The approach taken is somewhat informal owing to the wide variety of backgrounds of the readers, but the central ideas of backward error and sensitivity (conditioning) are systematically emphasized. The book is divided into four parts: Part I provides the background preliminaries including floating-point arithmetic, polynomials and computer evaluation of functions; Part II covers numerical linear algebra; Part III covers interpolation, the FFT and quadrature; and Part IV covers numerical solutions of differential equations including initial-value problems, boundary-value problems, delay differential equations and a brief chapter on partial differential equations. The book contains detailed illustrations, chapter summaries and a variety of exercises as well as some Matlab codes provided online as supplementary material. ?I really like the focus on backward error analysis and condition. This is novel in a textbook and a practical approach that will bring welcome attention." Lawrence F. Shampine. 606 $aComputer mathematics 606 $aNumerical analysis 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aComputer mathematics. 615 0$aNumerical analysis. 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aComputational Science and Engineering. 615 24$aNumerical Analysis. 676 $a004.0151 700 $aCorless$b Robert M$4aut$4http://id.loc.gov/vocabulary/relators/aut$0116752 702 $aFillion$b Nicolas$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910739414203321 996 $aA Graduate Introduction to Numerical Methods$93552877 997 $aUNINA