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| Name: | ||
| Miloslav Znojil | ||
| Reviewer number: | ||
| 9689 | ||
| Email: | ||
| znojil@ujf.cas.cz | ||
| Item's zbl-Number: | ||
| DE 018 485 897 | ||
| Author(s): | ||
| Strathopoulos, Andreas: | ||
| Shorttitle: | ||
| A case for a biorthogonal Jacobi-Davidson method: Restarting and correction equation | ||
| Source: | ||
| SIAM J. Matrix Anal. Appl. 24, No. 1, 238 - 259 | ||
| Classification: | ||
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| Primary Classification: | ||
| Secondary Classification: | ||
| Keywords: | ||
| Jacobi-Davidson; non-symmetric Lanczos; preconditioning; restarts; correction equation; three-term recurrences; BCG; eigenvalues; cubic convergence | ||
| Review: | ||
The non-symmetric Jacobi-Davidson (JD) methods do not seem to offer improvements based on a restarting scheme, while the mere alternative non-symmetric Lanczos algorithm itself, with restarts, does not make any use of a correction equation expanding its basis. At the same time, the multiplication of a vector by an adjoint of a matrix is ``cheap" on the contemporary parallelized computers. With these two ideas in mind, the author describes a combined method, a bi-orthogonal version of the JD approach, and brings arguments in favour of its high competitive potential: E.g., the JD convergence is improved from quadratic to cubic. | ||
| Remarks to the editors: | ||