Algorithms for computer algebra
Algorithms for computer algebra
Well … it isn't quite that simple
ACM SIGSAM Bulletin
Applied numerical linear algebra
Applied numerical linear algebra
Fraction-free algorithms for linear and polynomial equations
ACM SIGSAM Bulletin
The Turing factorization of a rectangular matrix
ACM SIGSAM Bulletin
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Simultaneous computation of the row and column rank profiles
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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The definition of the LU factoring of a matrix usually requires that the matrix be invertible. Current software systems have extended the definition to non-square and rank-deficient matrices, but each has chosen a different extension. Two new extensions, both of which could serve as useful standards, are proposed here: the first combines LU factoring with full-rank factoring, and the second extension combines full-rank factoring with fraction-free methods. Amongst other applications, the extension to full-rank, fraction-free factoring is the basis for a fractionfree computation of the Moore-Penrose inverse.