Jacobi-davidson type methods for generalized eigenproblems and polynomial eigenproblems
نویسندگان
چکیده
منابع مشابه
Jacobi-Davidson Methods for Symmetric Eigenproblems
1 Why and how The Lanczos method is quite eeective if the desired eigenvalue is either max or min and if this eigenvalue is relatively well separated from the remaining spectrum, or when the method is applied with (A ? I) ?1 , for some reasonable guess for an eigenvalue. If none of these conditions is fulllled, for instance the computation of a vector (A ? I) ?1 y for given y may be computation...
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We present a parallel implementation of the Davidson method for the numerical solution of large-scale, sparse, generalized eigenvalue problems. The implementation is done in the context of SLEPc, the Scalable Library for Eigenvalue Problem Computations. In this work, we focus on the Hermitian version of the method, with several optimizations. We compare the developed solver with other available...
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Iterative methods often provide the only means of solving large eigenvalue problems. Their block variants converge slowly but they are robust especially in the presence of multiplicities. Precon-ditioning is often used to improve convergence. Yet, for large matrices, the demands posed on the available computing resources are huge. Clusters of workstations and SMPs are becoming the main computat...
متن کاملA New Justification of the Jacobi–davidson Method for Large Eigenproblems
The Jacobi–Davidson method is known to converge at least quadratically if the correction equation is solved exactly, and it is common experience that the fast convergence is maintained if the correction equation is solved only approximately. In this note we derive the Jacobi–Davidson method in a way that explains this robust behavior.
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ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 1996
ISSN: 0006-3835,1572-9125
DOI: 10.1007/bf01731936