矩阵计算(Matri computation)英文版

最好的英文版本,PDF格式 原书名： Matrix Computations 原出版社： The Johns Hopkins University Press 作者： (美)Gene H. Golub Charles F. Van Loan Gene H.Golub，（1932-2007），美国科学院、工程院和艺术科学院院士，世界著名的数分析专家，现代矩阵计算的奠基人，生前曾任斯坦福大学教授。他是矩阵分解算法的主要贡献者，与William Kahan在1970年给出了奇异值分解（SingularValue Decomposition,SVD）的可行算法，一直沿用至今。他发起组织了工业与应用数学国际会议（Intemational Congress on Industrial and Applied Mathematics，ICIAM）。 目录回到顶部↑matrix multiplication problems . 1.1 basic algorithms and notation 2 1.2 exploiting structure 16 1.3 block matrices and algorithms 24 1.4 vectorization and re-use issues 34 2 matrix analysis 2.1 basic ideas from linear algebra 48 2.2 vector norms 52 2.3 matrix norms 54 2.4 finite precision matrix computations 59 2.5 orthogonality and the svd 69 2.6 projections and the cs decomposition 75 2.7 the sensitivity of square linear systems 80 3 general linear systems 3.1 triangular systems 88 3.2 the lu factorization 94 3.3 roundoff analysis of gaussian elimination 104 3.4 pivoting 109 3.5 improving and estimating accuracy 123 4 special linear systems .4.1 the ldmt and ldlt factorizations 135 4.2 positive definite systems 140 4.3 banded systems 152 4.4 symmetric indefinite systems 161 4.5 block systems 174 4.6 vandermonde systems and the fft 183 4.7 toeplitz and related systems 193 5 orthogonalization and least squares 5.1 householder and givens matrices 208 5.2 the qr factorization 223 5.3 the full rank ls problem 236 5.4 other orthogonal factorizations 248 5.5 the rank deficient ls problem 256 5.6 weighting and iterative improvement 264 5.7 square and underdetermined systems 270 6 parallel matrix computations 6.1 basic concepts 276 6.2 matrix multiplication 292 6.3 factorizations 300 7 the unsymmetric eigenvalue problem .. 7.1 properties and decompositions 310 7.2 perturbation theory 320 7.3 power iterations 330 7.4 the hessenberg and real schur forms 341 7.5 the practical qr algorithm 352 7.6 invariant subspace computations 362 7.7 the