LEADER 07690nam 2201945Ia 450 001 9910780861503321 005 20230120110119.0 010 $a1-282-45801-9 010 $a1-282-93607-7 010 $a9786612458019 010 $a1-4008-3388-4 024 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(MiAaPQ)EBC483513 035 $a(MiAaPQ)EBC4968574 035 $a(PPN)18795464X 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$b[electronic resource] /$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 $a0-691-14341-2 320 $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 610 $aAlgorithm. 610 $aAnalysis of algorithms. 610 $aAnalytic function. 610 $aAsymptotic analysis. 610 $aBasis (linear algebra). 610 $aBasis function. 610 $aBiconjugate gradient method. 610 $aBidiagonal matrix. 610 $aBilinear form. 610 $aCalculation. 610 $aCharacteristic polynomial. 610 $aChebyshev polynomials. 610 $aCoefficient. 610 $aComplex number. 610 $aComputation. 610 $aCondition number. 610 $aConjugate gradient method. 610 $aConjugate transpose. 610 $aCross-validation (statistics). 610 $aCurve fitting. 610 $aDegeneracy (mathematics). 610 $aDeterminant. 610 $aDiagonal matrix. 610 $aDimension (vector space). 610 $aEigenvalues and eigenvectors. 610 $aEquation. 610 $aEstimation. 610 $aEstimator. 610 $aExponential function. 610 $aFactorization. 610 $aFunction (mathematics). 610 $aFunction of a real variable. 610 $aFunctional analysis. 610 $aGaussian quadrature. 610 $aHankel matrix. 610 $aHermite interpolation. 610 $aHessenberg matrix. 610 $aHilbert matrix. 610 $aHolomorphic function. 610 $aIdentity matrix. 610 $aInterlacing (bitmaps). 610 $aInverse iteration. 610 $aInverse problem. 610 $aInvertible matrix. 610 $aIteration. 610 $aIterative method. 610 $aJacobi matrix. 610 $aKrylov subspace. 610 $aLaguerre polynomials. 610 $aLanczos algorithm. 610 $aLinear differential equation. 610 $aLinear regression. 610 $aLinear subspace. 610 $aLogarithm. 610 $aMachine epsilon. 610 $aMatrix function. 610 $aMatrix polynomial. 610 $aMaxima and minima. 610 $aMean value theorem. 610 $aMeromorphic function. 610 $aMoment (mathematics). 610 $aMoment matrix. 610 $aMoment problem. 610 $aMonic polynomial. 610 $aMonomial. 610 $aMonotonic function. 610 $aNewton's method. 610 $aNumerical analysis. 610 $aNumerical integration. 610 $aNumerical linear algebra. 610 $aOrthogonal basis. 610 $aOrthogonal matrix. 610 $aOrthogonal polynomials. 610 $aOrthogonal transformation. 610 $aOrthogonality. 610 $aOrthogonalization. 610 $aOrthonormal basis. 610 $aPartial fraction decomposition. 610 $aPolynomial. 610 $aPreconditioner. 610 $aQR algorithm. 610 $aQR decomposition. 610 $aQuadratic form. 610 $aRate of convergence. 610 $aRecurrence relation. 610 $aRegularization (mathematics). 610 $aRotation matrix. 610 $aSingular value. 610 $aSquare (algebra). 610 $aSummation. 610 $aSymmetric matrix. 610 $aTheorem. 610 $aTikhonov regularization. 610 $aTrace (linear algebra). 610 $aTriangular matrix. 610 $aTridiagonal matrix. 610 $aUpper and lower bounds. 610 $aVariable (mathematics). 610 $aVector space. 610 $aWeight function. 615 0$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 Ge?rard A$0431205 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780861503321 996 $aMatrices, moments and quadrature with applications$91408806 997 $aUNINA