===firstname:
Ruipeng
===firstname3:
Eugene
===affil6:

===lastname3:
Vecharynski
===email:
li50@llnl.gov
===keyword_other2:

===lastname6:

===affil5:
Department of Computer Science & Engineering, University of Minnesota, Twin Cities
===lastname4:
Yang
===lastname7:

===affil7:

===postal:
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P. O. Box 808, L-561, Livermore, CA 94551
===ABSTRACT:
Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum.  This work presents  a  technique for tackling this problem by combining  a Thick-Restart  version  of the  Lanczos algorithm  with  deflation (`locking')  and  a new type of polynomial filters. Thick restarting is employed to limit the cost of orthogonalization. The polynomial filter that maps eigenvalues within a given interval to eigenvalues with the largest magnitude of the transformed problem, is obtained from a least-squares approximation to an appropriately centered Dirac-$\delta$ distribution. The resulting algorithm
can be  utilized in a  `spectrum-slicing' approach whereby a 
very large  number of eigenvalues  and associated eigenvectors  of the matrix are computed by extracting eigenpairs located in different sub-intervals independently from one another. Numerical experiments show that such a construction yields effective polynomial filters which along with a Thick-Restart Lanczos procedure enable desired eigenpairs to be computed efficiently.
===affil3:
Computational Research Division, Lawrence Berkeley National Laboratory
===title:
A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems
===affil2:
Department of Computer Science & Engineering, University of Minnesota, Twin Cities
===lastname2:
Xi
===firstname4:
Chao
===keyword1:
Eigenvalue and singular value methods and applications
===workshop:
no
===lastname:
Li
===firstname5:
Yousef
===keyword2:
NOT_SPECIFIED
===otherauths:

===affil4:
Computational Research Division, Lawrence Berkeley National Laboratory
===competition:
no
===firstname7:

===firstname6:

===keyword_other1:

===lastname5:
Saad
===affilother:

===firstname2:
Yuanzhe