On bounds for symmetric eigenvalue problems

1983 ◽  
pp. 195-205
Author(s):  
Alan Jennings
Keyword(s):  
Eigenvalue Problems ◽  
Symmetric Eigenvalue Problems

A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

2017 ◽  
Vol 7 (1) ◽  
pp. 21-37 ◽  
Author(s):  
Cun-Qiang Miao
Keyword(s):  
Convergence Rate ◽  
Chebyshev Polynomials ◽  
Numerical Experiments ◽  
Eigenvalue Problems ◽  
Cubic Convergence ◽  
Davidson Method ◽  
Filtering Technique ◽  
Matrix Vector ◽  
Three Term Recurrence Relation ◽  
Symmetric Eigenvalue Problems

AbstractFor symmetric eigenvalue problems, we constructed a three-term recurrence polynomial filter by means of Chebyshev polynomials. The new filtering technique does not need to solve linear systems and only needs matrix-vector products. It is a memory conserving filtering technique for its three-term recurrence relation. As an application, we use this filtering strategy to the Davidson method and propose the filtered-Davidson method. Through choosing suitable shifts, this method can gain cubic convergence rate locally. Theory and numerical experiments show the efficiency of the new filtering technique.

scholarly journals High performance solution of skew-symmetric eigenvalue problems with applications in solving the Bethe-Salpeter eigenvalue problem

2020 ◽  
Vol 96 ◽  
pp. 102639
Author(s):  
Carolin Penke ◽  
Andreas Marek ◽  
Christian Vorwerk ◽  
Claudia Draxl ◽  
Peter Benner
Keyword(s):  
Eigenvalue Problem ◽  
High Performance ◽  
Eigenvalue Problems ◽  
Symmetric Eigenvalue Problems
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