Abstract
The stability of the computational process in the solution of systems of linear algebraic equations Ax=b by the GE depends on the condition number of matrix A. Reliable and efficient algorithms for calculating estimates of the condition number of a matrix are given in [43]. The application of these algorithms in sparse matrix software (the code actually used is package Y12M, [331,341] but the same ideas could be applied for other codes also) is discussed in this chapter. Three algorithms have been implemented in Y12M and tested on a very large set of problems. The influence of the stability factor u that is used in the pivotal strategy (see Chapter 4) and the drop-tolerance T (see Chapter 5) on the accuracy of the estimates of the condition number is also studied.
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© 1991 Springer Science+Business Media Dordrecht
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Zlatev, Z. (1991). Condition Number Estimators in a Sparse Matrix Software. In: Computational Methods for General Sparse Matrices. Mathematics and Its Applications, vol 65. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1116-6_9
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DOI: https://doi.org/10.1007/978-94-017-1116-6_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4086-2
Online ISBN: 978-94-017-1116-6
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