The Null Space Problem II. Algorithms
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[For part I see ibid. 7, 527-537 (1986; Zbl 0608.65024).] Two algorithms are suggested for calculating a sparse basis of the null- space of matrix with full row rank. Each consists of the two phases: first (the combinatorial phase) identifies a minimal dependent set of columns by finding a matching in the bipartite graph of the matrix; second (the numerical, and more time-consuming, phase) calculates nonzero coefficients of the null-vectors from this dependent set. Linear independency is ensured by restricting a basis to be triangular or fundamental (with an identity matrix). Numerical results and experience are presented.
Computational methods for sparse matrices, Numerical mathematical programming methods, Nonlinear programming, sparse matrices, bipartite graph, Other matrix algorithms, Numerical results, linear programming, null-space, combinatorial phase
Computational methods for sparse matrices, Numerical mathematical programming methods, Nonlinear programming, sparse matrices, bipartite graph, Other matrix algorithms, Numerical results, linear programming, null-space, combinatorial phase
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