Computing Approximate Eigenpairs of Symmetric Block Tridiagonal Matrices

2003 ◽  
Vol 25 (1) ◽  
pp. 65-85 ◽  
Author(s):  
Wilfried N. Gansterer ◽  
Robert C. Ward ◽  
Richard P. Muller ◽  
William A. Goddard
Keyword(s):  
Tridiagonal Matrices ◽  
Symmetric Block

scholarly journals Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 870
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Functional Analysis ◽  
Computer Algebra ◽  
Toeplitz Matrices ◽  
Test Cases ◽  
Recursive Procedure ◽  
Tridiagonal Matrices ◽  
Special Cases ◽  
The Matrix ◽  
Matrix Eigenvalues ◽  
Complex Valued

We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©.

RationalQR transformation with Newton shift for symmetric tridiagonal matrices

1968 ◽  
Vol 11 (3) ◽  
pp. 264-272 ◽  
Author(s):  
C. Reinsch ◽  
F. L. Bauer
Keyword(s):  
Tridiagonal Matrices

scholarly journals Efficient computation of tridiagonal matrices largest eigenvalue

2018 ◽  
Vol 330 ◽  
pp. 268-275 ◽  
Author(s):  
Diego F.G. Coelho ◽  
Vassil S. Dimitrov ◽  
L. Rakai
Keyword(s):  
Efficient Computation ◽  
Largest Eigenvalue ◽  
Tridiagonal Matrices
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