LEADER 04358nam 2200829Ia 450 001 9910965467003321 005 20240912161638.0 010 $a9786612458019 010 $a9781282458017 010 $a1282458019 010 $a9781282936072 010 $a1282936077 010 $a9781400833887 010 $a1400833884 024 7 $a10.1515/9781400833887 035 $a(CKB)2520000000007012 035 $a(EBL)483513 035 $a(OCoLC)697182001 035 $a(SSID)ssj0000459484 035 $a(PQKBManifestationID)11328490 035 $a(PQKBTitleCode)TC0000459484 035 $a(PQKBWorkID)10473240 035 $a(PQKB)11606634 035 $a(DE-B1597)446937 035 $a(OCoLC)979577116 035 $a(DE-B1597)9781400833887 035 $a(Au-PeEL)EBL483513 035 $a(CaPaEBR)ebr10364784 035 $a(CaONFJC)MIL293607 035 $a(Au-PeEL)EBL4968574 035 $a(CaONFJC)MIL245801 035 $z(PPN)199244391 035 $a(PPN)18795464X 035 $a(FR-PaCSA)88838008 035 $a(MiAaPQ)EBC483513 035 $a(MiAaPQ)EBC4968574 035 $a(Perlego)734794 035 $a(FRCYB88838008)88838008 035 $a(EXLCZ)992520000000007012 100 $a20091015d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMatrices, moments, and quadrature with applications /$fGene H. Golub and Gerard Meurant 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$dc2010 215 $a1 online resource (376 p.) 225 1 $aPrinceton series in applied mathematics 300 $aDescription based upon print version of record. 311 08$a9780691143415 311 08$a0691143412 320 $aIncludes bibliographical references (p. 335-359) and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tPART 1. Theory -- $tChapter 1. Introduction -- $tChapter 2. Orthogonal Polynomials -- $tChapter 3. Properties of Tridiagonal Matrices -- $tChapter 4. The Lanczos and Conjugate Gradient Algorithms -- $tChapter 5. Computation of the Jacobi Matrices -- $tChapter 6. Gauss Quadrature -- $tChapter 7. Bounds for Bilinear Forms uT?(A)v -- $tChapter 8. Extensions to Nonsymmetric Matrices -- $tChapter 9. Solving Secular Equations -- $tPART 2. Applications -- $tChapter 10. Examples of Gauss Quadrature Rules -- $tChapter 11. Bounds and Estimates for Elements of Functions of Matrices -- $tChapter 12. Estimates of Norms of Errors in the Conjugate Gradient Algorithm -- $tChapter 13. Least Squares Problems -- $tChapter 14. Total Least Squares -- $tChapter 15. Discrete Ill-Posed Problems -- $tBibliography -- $tIndex 330 $aThis computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms. 410 0$aPrinceton series in applied mathematics. 606 $aMatrices 606 $aNumerical analysis 615 0$aMatrices. 615 0$aNumerical analysis. 676 $a512.9434 686 $aSK 915$2rvk 700 $aGolub$b Gene H$g(Gene Howard),$f1932-2007.$07784 701 $aMeurant$b Gerard A$0431205 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910965467003321 996 $aMatrices, moments and quadrature with applications$91408806 997 $aUNINA