Direct Methods for Sparse Linear Systems
Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages. With a strong emphasis on MATLAB® and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.
allocate result array beta block breadth-first search check inputs column counts compressed-column computes const int cs_amd cs_chol CS_CSC cs_dmperm cs_done cs_free cs_lsolve cs_lu cs_malloc cs_spfree cs_sprealloc cs_sqr data structure denote dense depth-first search directed graph Duff Dulmage-Mendelsohn decomposition elimination tree fcth Fiedler vector frontal matrix ftft graph hash bucket Householder reflection in/out iteration left-looking linear loop lower triangular MATLAB equivalent MATLAB statement maximum matching method mexFunction multifrontal node nonzero pattern NULL on error number of entries nzmax parent partial pivoting path permutation matrix permutation vector pinv postordering printf QR factorization recursion return NULL right-looking row and column row subtree S->pinv sizeof int sparse Cholesky factorization sparse LU factorization sparse matrix stack strongly connected components structural rank supernodal symmetric symmetric matrix Theorem traversal triangular solve triangular system triplet form upper triangular void workspace zero entries zero-free diagonal
Page 200 - IS DUFF. Algorithm 575: Permutations for a zero-free diagonal, ACM Trans. Math. Software, 7 (1981), pp. 387-390.
Page iv - Editorial Board Peter Benner Dianne P. O'Leary Technische Universitat Chemnitz University of Maryland John R. Gilbert Robert D. Russell University of California, Santa Barbara Simon Fraser University Michael T. Heath Robert D. Skeel University of Illinois — Urbana-Champaign Purdue University CT Kelley Danny Sorensen North Carolina State University Rice University Cleve Moler Andrew J. Wathen The MathWorks, Inc.
Numerische Mathematik: Eine Einführung anhand von ...
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