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Linear algebra using Maple’s LargeExpressions package. (English) Zbl 1107.65029
Kotsireas, Ilias (ed.) et al., Maple conference 2006. Proceedings of the conference, Waterloo, Ontario, Canada, July 23–26, 2006. Waterloo: Maplesoft (ISBN 1-897310-13-7/pbk). 14-25 (2006).
Summary: The package LargeExpressions has been available in MAPLE for a number of years, but it is not well known. It provides tools for managing large expressions. In this paper, we describe a new application of this tool to the LU factoring of matrices. We describe a function that factors a matrix and expresses the results using a hierarchical representation. As part of the LU factoring, we introduce several strategies for pivoting, veiling an expression and zero-recognition in our function. All these strategies can be chosen based on the application. The new function is very flexible aud much faster than the existing LuDecomposition command in Maple. Results of benchmark calculations are given.
For the entire collection see [Zbl 1099.65001].
65F05 Direct numerical methods for linear systems and matrix inversion
65Y15 Packaged methods for numerical algorithms
68W30 Symbolic computation and algebraic computation