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A fast recursive orthogonalization scheme for the Macaulay matrix.
- Source :
-
Journal of Computational & Applied Mathematics . Sep2014, Vol. 267, p20-32. 13p. - Publication Year :
- 2014
-
Abstract
- Abstract: In this article we present a fast recursive orthogonalization scheme for two important subspaces of the Macaulay matrix: its row space and null space. It requires a graded monomial ordering and exploits the resulting structure of the Macaulay matrix induced by this graded ordering. The resulting orthogonal basis for the row space will retain a similar structure as the Macaulay matrix and is as a consequence sparse. The computed orthogonal basis for the null space is dense but typically has smaller dimensions. Two alternative implementations for the recursive orthogonalization scheme are presented: one using the singular value decomposition and another using a sparse rank revealing multifrontal QR decomposition. Numerical experiments show the effectiveness of the proposed recursive orthogonalization scheme in both running time and required memory compared to a standard orthogonalization. The sparse multifrontal QR implementation is superior in both total run time and required memory at the cost of being slightly less reliable for determining the numerical rank. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 267
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 95222065
- Full Text :
- https://doi.org/10.1016/j.cam.2014.01.035