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Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix

Author
Encinas, A.; Jiménez, M.J.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2017-06-12
Volume
542
First page
402
Last page
421
DOI
https://doi.org/10.1016/j.laa.2017.06.010 Open in new window
Project funding
The effective resistance as a tool for the study of the inverse problem of the conductances and the analysis of the perturbations on networks
Repository
http://hdl.handle.net/2117/106362 Open in new window
URL
http://www.sciencedirect.com/science/article/pii/S0024379517303737 Open in new window
Abstract
We have named tridiagonal (p,r)–Toeplitz matrix to those tridiagonal matrices in which each diagonal is a quasi–periodic sequence, d(p+j)=rd(j), so with period p¿N but multiplied by a real number r. We present here the necessary and sufficient conditions for the invertibility of this kind of matrices and explicitly compute their inverse. The techniques we use are related with the solution of boundary value problems associated to second order linear difference equations. These boundary value...
Citation
Encinas, A., Jiménez, M.J. Explicit inverse of a tridiagonal (p,r)-Toeplitz matrix. "Linear algebra and its applications", Vol. 542, 01 Abril, 2018, p. 402-421.
Keywords
boundary value problems, discrete Schrödinger operator, quasi–periodic sequences, second order linear difference equations, tridiagonal matrices
Group of research
MAPTHE - Matrix Analysis and Discrete Potential Theory