Trace inverse algorithms for the general eigenvalue problem

2003 ◽  
Author(s):  
M.A. Hasan ◽  
A.A. Hasan
Keyword(s):  
Eigenvalue Problem ◽  
General Eigenvalue Problem

On the shifted eigenvalue problem

1970 ◽  
Vol 67 (1) ◽  
pp. 97-99 ◽  
Author(s):  
R. J. Bell ◽  
P. Dean
Keyword(s):  
State Physics ◽  
Solid State ◽  
Eigenvalue Problem ◽  
Solid State Physics ◽  
General Eigenvalue Problem ◽  
Image Position

Lanczos(1, 2) has considered the shifted eigenvalue problem where C is a (p × q) matrix of rank r, CH is its hermitean conjugate and u, v are column vectors of orders p, q respectively. In this note we extend Lanczos' work to cover the more general eigenvalue problem which arises in certain problems in solid state physics (3). In (2), the I's are unit matrices of appropriate orders and the constants a, b are real; the partitioned matrix M is thus hermitean so that its eigenvalues λ are real.

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