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Explicit inverse of nonsingular Jacobi matrices

Author
Encinas, A.; Jiménez, M.J.
Type of activity
Journal article
Journal
Discrete applied mathematics
Date of publication
2019-06-30
Volume
263
First page
130
Last page
139
DOI
10.1016/j.dam.2019.03.005
Project funding
A multifaced approach to !he inverse problems on Networks: Eigenvalues, conductance recovering and numerical algorithms
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://arxiv.org/abs/1807.07642 Open in new window
http://hdl.handle.net/2117/130869 Open in new window
URL
https://www.sciencedirect.com/science/article/pii/S0166218X19301556 Open in new window
Abstract
We present here the necessary and sufficient conditions for the invertibility of tridiagonal matrices, commonly named Jacobi matrices, and explicitly compute their inverse. The techniques we use are related with the solution of Sturm–Liouville boundary value problems associated to second order linear difference equations. These boundary value problems can be expressed throughout a discrete Schrödinger operator and their solutions can be computed using recent advances in the study of linear di...
Citation
Encinas, A.; Jiménez, M.J. Explicit inverse of nonsingular Jacobi matrices. "Discrete applied mathematics", 30 Juny 2019, vol. 263, p. 130-139.
Keywords
Chebyshev functions and polynomials, Discrete Schrödinger operator, Second order linear difference equations, Sturm–Liouville boundary value problems, Tridiagonal matrices
Group of research
MAPTHE - Matrix Analysis and Discrete Potential Theory