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.
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ACM Trans allocate result beta block check inputs Cited 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 cs_transpose data structure decomposition deﬁned dense depth-ﬁrst search directed graph Duff edge elimination tree etree Fiedler vector ﬁle ﬁll-reducing ﬁnds ﬁrst frontal matrix function Gaussian elimination graph hash bucket hhead iteration kth row left-looking lower triangular LU factorization Math MATLAB equivalent Matrix Anal maximum matching method mexFunction modiﬁed multifrontal node nonzero pattern NULL on error number of entries nzmax parent partial pivoting path permutation matrix permutation vector pinv postordering printf recursion return NULL row and column row subtree SIAM sizeof int Software sparse Cholesky factorization sparse matrix sparse QR factorization stack strongly connected components structural rank supernodal symmetric symmetric matrix Theorem traversal triplet form upper triangular void workspace