Mohr M, Popa C, Rüde U (2004)
Publication Type: Journal article
Publication year: 2004
Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles
Book Volume: 81
Pages Range: 215-226
Journal Issue: 2
DOI: 10.1080/00207160310001650134
In a previous article, one of the authors presented an extension of an iterative approximate orthogonalisation algorithm, due to Z. Kovarik, for arbitrary rectangular matrices. In the present article, we propose a modified version of this extension for the class of arbitrary symmetric matrices. For this new algorithm, the computational effort per iteration is much smaller than for the initial one. We prove its convergence and also derive an error reduction factor per iteration. In the second part of the article, we show that we can eliminate the matrix inversion required by the previous algorithm in each iteration, by replacing it with a polynomial matrix expression. Some numerical experiments are also presented for a collocation discretisation of a first kind integral equation.
APA:
Mohr, M., Popa, C., & Rüde, U. (2004). An Iterative Algorithm for Approximate Orthogonalisation of Symmetric Matrices. International Journal of Computer Mathematics, 81(2), 215-226. https://dx.doi.org/10.1080/00207160310001650134
MLA:
Mohr, Marcus, Constantin Popa, and Ulrich Rüde. "An Iterative Algorithm for Approximate Orthogonalisation of Symmetric Matrices." International Journal of Computer Mathematics 81.2 (2004): 215-226.
BibTeX: Download