数值线性代数及其应用_PDF下载[98MB-百度云]Xiao-qingJin，Yi-min

本书特色

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Numerical linear algebra， also called matrix computation， has beea cen-ter of scientific and engineering computing since 1946， the first modercom-puter was born. Most of problems iscience and engineering finally becomeproblems imatrix computation. Therefore， it is important for us to study nu-merical linear algebra. This book gives aelementary introductioto matrixcomputatioand it also includes some new results obtained irecent years.

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PrefaceChapter 1 Introduction1．1 Basic symbols1．2 Basic problems iNLA1．3 Why shall we study numerical methods?1．4 Matrix factorizations (decompositions)1．5 Perturbatioand error analysis1．6 Operatiocost and convergence rateExercisesChapter 2 Direct Methods for Linear Systems2．1 Triangular linear systems and LU factorization2．2 LU factorizatiowith pivoting2．3 Cholesky factorizationExercisesChapter 3 Perturbatioand Error Analysis3．1 Vector and matrix norms3．2 Perturbatioanalysis for linear systems3．3 Error analysis ofloating point arithmetic3．4 Error analysis opartial pivotingExercisesChapter 4 Least Squares Problems4．1 Least squares problems4．2 Orthogonal transformations4．3 QR decompositionExercisesChapter 5 Classical Iterative Methods5．1 Jacobi and Gauss-Seidel method5．2 Convergence analysis5．3 Convergence rate5．4 SOR methodExercisesChapter 6 Krylov Subspace Methods6．1 Steepest descent method6．2 Conjugate gradient method6．3 Practical CG method and convergence analysis6．4 Preconditioning6．5 GMRES methodExercisesChapter 7 Nonsymmetric Eigenvalue Problems7．1 Basic properties7．2 Power method7．3 Inverse power method7．4 QR method7．5 Real versioof QR algorithmExercisesChapter 8 Symmetric Eigenvalue Problems8．1 Basic spectral properties8．2 Symmetric QR method8．3 Jacobi method8．4 Bisectiomethod8．5 Divide-and-conquer methodExercisesChapter 9 ApplicationsBibliographyIndex