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Globally convergent Jacobi methods for positive definite matrix pairs.
- Source :
- Numerical Algorithms; Sep2018, Vol. 79 Issue 1, p221-249, 29p
- Publication Year :
- 2018
-
Abstract
- The paper derives and investigates the Jacobi methods for the generalized eigenvalue problem Ax = λBx, where A is a symmetric and B is a symmetric positive definite matrix. The methods first “normalize” B to have the unit diagonal and then maintain that property during the iterative process. The global convergence is proved for all such methods. That result is obtained for the large class of generalized serial strategies from Hari and Begović Kovač (Trans. Numer. Anal. (ETNA) 47, 107-147, 2017). Preliminary numerical tests confirm a high relative accuracy of some of those methods, provided that both matrices are positive definite and the spectral condition numbers of Δ<subscript>A</subscript>AΔ<subscript>A</subscript>and Δ<subscript>B</subscript>BΔ<subscript>B</subscript>are small, for some nonsingular diagonal matrices Δ<subscript>A</subscript>and Δ<subscript>B</subscript>. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10171398
- Volume :
- 79
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Numerical Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 131406297
- Full Text :
- https://doi.org/10.1007/s11075-017-0435-5