Rayleigh quotient minimization method for symmetric eigenvalue problems

2019 ◽  
Vol 38 (4) ◽  
Author(s):  
Cun-Qiang Miao ◽  
Hao Liu
Keyword(s):  
Eigenvalue Problems ◽  
Rayleigh Quotient ◽  
Minimization Method ◽  
Symmetric Eigenvalue Problems

scholarly journals A Rayleigh quotient method for criticality eigenvalue problems in neutron transport

2020 ◽  
Vol 138 ◽  
pp. 107120
Author(s):  
M.I. Ortega ◽  
R.N. Slaybaugh ◽  
P.N. Brown ◽  
T.S. Bailey ◽  
B. Chang
Keyword(s):  
Eigenvalue Problems ◽  
Neutron Transport ◽  
Rayleigh Quotient

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.

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