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- W2002136992 abstract "In the tableau approach to large-electrical-network analysis, as well as in structure analysis, the finite-element method, linear programming etc., a very sparse linear algebraic set of equations Ax = b has to be solved repeatedly. To efficiently solve the system via Gaussian elimination, an optimization problem has to be faced: the selection of a pivot strategy to maintain the sparsity of the matrix A. It is possible also to follow a different strategy to fully exploit the sparsity of A, i.e. to transform A into an equivalent but more convenient form. Both of these problems have been studied and partially solved by means of directed graphs associated with A when symmetric permutations on A are allowed.In this paper, a graph theoretical interpretation has been given to nonsymmetric permutations on A, which can be considered a fundamental step towards the solution of the above-mentioned optimization problems. This interpretation is obtained through decomposition theorems on nonsymmetric permutations, correspondence theorems between column (row) permutations and topological operations on a directed graph representing A." @default.
- W2002136992 created "2016-06-24" @default.
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- W2002136992 date "1977-04-01" @default.
- W2002136992 modified "2023-09-23" @default.
- W2002136992 title "A graph theoretical interpretation of nonsymmetric permutation on sparse matrices" @default.
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- W2002136992 doi "https://doi.org/10.1002/cta.4490050206" @default.
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