Matrix Algorithms: Volume 1: Basic DecompositionsSIAM, 1 aug 1998 - 477 pagina's This thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions - the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the computation and applications of the LU and QR decompositions. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. A certain knowledge of elementary analysis and linear algebra is assumed, as well as a reasonable amount of programming experience. The guiding principle, that if something is worth explaining, it is worth explaining fully, has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study. |
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algorithm analysis applied approximation arithmetic array backward basis block bound called Chapter columns complete components computed condition Consequently consider contains corresponding count defined determine diagonal effects elements equations error estimate example fact factorization Figure first flam function Gaussian elimination given gives Gram—Schmidt Hence Householder transformations implementation important introduce inverse iterative least squares problem linear systems loop matrix memory method multipliers nonsingular nonzero norm normal Note observation obtain operations original orthogonal orthogonal matrix partitioned perform perturbation pivoting positive definite problem proof QR decomposition QR factorization rank reason reduced references relation represents requires result rotations scaling Schur complement sequence shows singular values solution solve space stability statement step stored subspaces suppose Theorem treat triangular unit updating upper vector write zero