Abstract
This chapter discusses the elementary operations of sparse matrix algebra—transposition, permutation of rows and columns, ordering of a sparse representation, addition and multiplication of two sparse matrices, and multiplication of a sparse matrix and a vector. The chapter reviews the triangular factorization of a symmetric positive definite sparse matrix, where diagonal pivoting is numerically stable, and sparse forward and backward substitution. The chapter discusses the algorithmic aspects of elimination in the case where the lower triangle of the matrix, which contains the nonzero elements to be eliminated, is not explicitly stored in the computer, and the row-wise format makes column scanning difficult to program efficiently. Sparse matrix algebra is an important part of sparse matrix technology. There are abundant examples of algorithms that employ operations with sparse matrices—hypermatrix and supersparse techniques, assembly of finite element equations, ordering of a row-wise representation before Gauss elimination, and many others.
Published Version
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