Restarting from Specific Points to Cure Breakdown in Lanczos-type Algorithms
نویسندگان
چکیده
منابع مشابه
A Switching Approach to Avoid Breakdown in Lanczos-Type Algorithms
Lanczos-type algorithms are well known for their inherent instability. They typically breakdown when relevant orthogonal polynomials do not exist. Current approaches to avoiding breakdown rely on jumping over the non-existent polynomials to resume computation. This jumping strategy may have to be used many times during the solution process. We suggest an alternative to jumping which consists in...
متن کاملa preemptive restarting approach to beating the inherent instability of lanczos-type algorithms
lanczos-type algorithms are well known for their inherent instability. they typically breakdown occurs when relevant orthogonal polynomials do not exist. current approaches to curing breakdown rely on jumping over the non-existent polynomials to resume computation. this may have to be used many times during the solution process. we suggest an alternative to jumping, which consists of restarting...
متن کاملNested Lanczos : Implicitly Restarting a Lanczos Algorithm Nested Lanczos : Implicitly Restarting a Lanczos Algorithm
In this text, we present a generalisation of the idea of the Implicitly Restarted Arnoldi method to the nonsymmetric Lanczos algorithm, using the two-sided Gram-Schmidt process or using a full Lanczos tridi-agonalisation. The Implicitly Restarted Lanczos method can be combined with an implicit lter. It can also be used in case of breakdown and ooers an alternative for look-ahead.
متن کاملImplicitly Restarting Lanczos
We show in this text how the idea of the Implicitly Restarted Arnoldi method can be generalised to the non-symmetric Lanczos algorithm, using the two-sided Gram-Schmidt process or using a Lanczos tridiagonalisation. The implicitly restarted Lanczos method can be combined with an implicit lter. It can also be used in case of breakdown and ooers an alternative for look-ahead.
متن کاملRestarting the Nonsymmetric Lanczos Algorithm
A restarted nonsymmetric Lanczos algorithm is given for computing eigenvalus and both right and left eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Restarting also makes it possible to deal with roundoff error in new ways. We give a scheme for avoiding near-breakdown and discuss maintaining biorthogonality. A system of linear equations can be solved s...
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ژورنال
عنوان ژورنال: Journal of Mathematical and Fundamental Sciences
سال: 2015
ISSN: 2337-5760,2338-5510
DOI: 10.5614/j.math.fund.sci.2015.47.2.5