scholarly journals The eigenvalue problem for infinite complex symmetric tridiagonal matrices with application

1996 ◽  
Vol 241-243 ◽  
pp. 599-618 ◽  
Author(s):  
Yasuhiko Ikebe ◽  
Nobuyoshi Asai ◽  
Yoshinori Miyazaki ◽  
DongSheng Cai
Keyword(s):  
Eigenvalue Problem ◽  
Tridiagonal Matrices ◽  
Complex Symmetric

scholarly journals An application of the homotopy method to the generalised symmetric eigenvalue problem

1988 ◽  
Vol 30 (2) ◽  
pp. 230-249
Author(s):  
Wen-Wei Lin ◽  
Gerhard Lutzer
Keyword(s):  
Eigenvalue Problem ◽  
Positive Definite ◽  
Homotopy Method ◽  
Smooth Curves ◽  
Symmetric Eigenvalue Problem ◽  
Tridiagonal Matrices ◽  
Almost All ◽  
Curve Tracing

AbstractThe homotopy method is used to find all eigenpairs of a generalised symmetric eigenvalue problem Ax = λBx with positive definite B. The determination of n eigenpairs (x, λ) is reduced to curve tracing of n disjoint smooth curves in Rn × R × [0, 1]. The method might be attractive if A and B are sparse symmetric. In this paper it is shown that the method will work for almost all symmetric tridiagonal matrices A and B.

Eigenvalue problem for tridiagonal matrices arising in the scattering-theory analysis of disordered conductors

1992 ◽  
Vol 70 (4) ◽  
pp. 257-267 ◽  
Author(s):  
Josef A. Zuk
Keyword(s):  
Eigenvalue Problem ◽  
Scattering Theory ◽  
Perturbation Expansion ◽  
Approximate Solutions ◽  
Theory Analysis ◽  
Tridiagonal Matrices ◽  
Finite Matrix ◽  
Special Cases ◽  
Exactly Solvable ◽  
Qualitative Characteristics

The eigenvalue problem for a family of tridiagonal matrices arising in the scattering-theory analysis of the conductance in mesoscopic systems, and its fluctuations, is studied. The exactly solvable special cases are identified. For the general problem, qualitative characteristics of the spectrum are established, and approximate solutions for the eigenvalues are constructed. These comprise ones that are valid in the limit of large but finite matrix dimension, and those derived from a perturbation expansion around each of the exactly solvable cases.

scholarly journals An inverse eigenvalue problem for symmetrical tridiagonal matrices

2007 ◽  
Vol 54 (5) ◽  
pp. 699-708 ◽  
Author(s):  
Hubert Pickmann ◽  
Ricardo L. Soto ◽  
J. Egaña ◽  
Mario Salas
Keyword(s):  
Eigenvalue Problem ◽  
Inverse Eigenvalue Problem ◽  
Tridiagonal Matrices ◽  
Inverse Eigenvalue
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