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A new version of Kovarik’s approximate orthogonalization algorithm without matrix inversion.
- Source :
-
International Journal of Computer Mathematics . Oct2005, Vol. 82 Issue 10, p1235-1246. 12p. - Publication Year :
- 2005
-
Abstract
- In 1970 Kovarik proposed approximate orthogonalization algorithms. One of them (algorithm B) has quadratic convergence but requires at each iteration the inversion of a matrix of similar dimension to the initial one. An attempt to overcome this difficulty was made by replacing the inverse with a finite Neumann series expansion involving the original matrix and its adjoint. Unfortunately, this new algorithm loses the quadratic convergence and requires a large number of terms in the Neumann series which results in a dramatic increase in the computational effort per iteration. In this paper we propose a much simpler algorithm which, by using only the first two terms in a different series expansion, gives us the desired result with linear convergence. Systematic numerical experiments for collocation and Toeplitz matrices are also described. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00207160
- Volume :
- 82
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- International Journal of Computer Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 18363816
- Full Text :
- https://doi.org/10.1080/00207160512331331174