The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems

1980 ◽  
Vol 35 (152) ◽  
pp. 1251 ◽  
Author(s):  
Thomas Ericsson ◽  
Axel Ruhe
Keyword(s):  
Numerical Solution ◽  
Eigenvalue Problems ◽  
Lanczos Method ◽  
Spectral Transformation ◽  
Symmetric Eigenvalue Problems

scholarly journals Numerical Solution of PDE Eigenvalue Problems

2013 ◽  
Vol 10 (4) ◽  
pp. 3221-3304 ◽  
Author(s):  
Andrew Knyazev ◽  
Volker Mehrmann ◽  
Jinchao Xu
Keyword(s):  
Numerical Solution ◽  
Eigenvalue Problems

scholarly journals A note on the Ritz method with an application to overtone stellar pulsation theory

1968 ◽  
Vol 8 (2) ◽  
pp. 275-286 ◽  
Author(s):  
A. L. Andrew
Keyword(s):  
Numerical Solution ◽  
Eigenvalue Problems ◽  
Ritz Method ◽  
Linear Operators ◽  
Matrix Equations ◽  
Infinite Dimensional ◽  
Stellar Pulsation ◽  
Finite Matrix ◽  
The Matrix ◽  
Matrix Eigenvalue Problems

The Ritz method reduces eigenvalue problems involving linear operators on infinite dimensional spaces to finite matrix eigenvalue problems. This paper shows that for a certain class of linear operators it is possible to choose the coordinate functions so that numerical solution of the matrix equations is considerably simplified, especially when the matrices are large. The method is applied to the problem of overtone pulsations of stars.

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