LEADER 03675nam 22006375 450 001 9910964618203321 005 20250811094756.0 010 $a9781475722727 010 $a1475722729 024 7 $a10.1007/978-1-4757-2272-7 035 $a(CKB)2660000000024209 035 $a(SSID)ssj0001297242 035 $a(PQKBManifestationID)11766177 035 $a(PQKBTitleCode)TC0001297242 035 $a(PQKBWorkID)11354710 035 $a(PQKB)11535601 035 $a(DE-He213)978-1-4757-2272-7 035 $a(MiAaPQ)EBC3084190 035 $a(PPN)238008606 035 $a(EXLCZ)992660000000024209 100 $a20130125d1993 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to Numerical Analysis /$fby J. Stoer, R. Bulirsch 205 $a2nd ed. 1993. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1993. 215 $a1 online resource (XIII, 660 p.) 225 1 $aTexts in Applied Mathematics,$x2196-9949 ;$v12 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a9780387978789 311 08$a038797878X 311 08$a9781475722741 311 08$a1475722745 320 $aIncludes bibliographical references and index. 327 $a1 Error Analysis -- 2 Interpolation -- 3 Topics in Integration -- 4 Systems of Linear Equations -- 5 Finding Zeros and Minimum Points by Iterative Methods -- 6 Eigenvalue Problems -- 7 Ordinary Differential Equations -- 8 Iterative Methods for the Solution of Large Systems of Linear Equations. Some Further Methods -- General Literature on Numerical Methods. 330 $aOn the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa­ tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations. 410 0$aTexts in Applied Mathematics,$x2196-9949 ;$v12 606 $aNumerical analysis 606 $aNumerical Analysis 615 0$aNumerical analysis. 615 14$aNumerical Analysis. 676 $a518 676 $a518 686 $a65-01$2msc 700 $aStoer$b Josef$4aut$4http://id.loc.gov/vocabulary/relators/aut$012949 702 $aBulirsch$b Roland$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910964618203321 996 $aIntroduction to numerical analysis$91501478 997 $aUNINA