Topic
Tridiagonal matrix algorithm
About: Tridiagonal matrix algorithm is a research topic. Over the lifetime, 1070 publications have been published within this topic receiving 21084 citations.
Papers published on a yearly basis
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Papers
TL;DR: The results are constructive, in the sense that they generate an algorithmic procedure to construct the matrix from the minimal and maximal eigenvalues of all its leading principal submatrices.
Abstract: We consider the following inverse eigenvalue problem: to construct a symmetrical tridiagonal matrix from the minimal and maximal eigenvalues of all its leading principal submatrices. We give a necessary and sufficient condition for the existence of such a matrix and for the existence of a nonnegative symmetrical tridiagonal matrix. Our results are constructive, in the sense that they generate an algorithmic procedure to construct the matrix.
28 citations
TL;DR: In this paper, the tridiagonal matrices of Sylvester type were explicitly determined and they are closely related to orthogonal polynomials named after Krawtchouk, (dual) Hahn and Racah.
Abstract: Eigenvectors of the tridiagonal matrices of Sylvester type are explicitly determined. These are closely related to orthogonal polynomials named after Krawtchouk, (dual) Hahn and Racah as well as to q-Racah polynomials.
28 citations
TL;DR: An alternating direction implicit (ADI) scheme for the wide-angle finite-difference beam propagation method (FD-BPM) based on the wide angled Pade multistep method is presented in this article.
Abstract: An alternating direction implicit (ADI), scheme for the wide-angle finite-difference beam propagation method (FD-BPM) based on the wide angled Pade multistep method is presented. The scheme incorporates an iterative technique for correction of the operator splitting error. The resulting equations are efficiently solved by the Thomas algorithm for tri-diagonal band matrices. The dispersion characteristics, accuracy and stability of the scheme is verified analytically and numerically for the cases of a plane wave propagating at fixed angle to the assumed propagation direction of the algorithm and the three dimensional angled propagation of a Gaussian beam. The computational requirements of the method are assessed against a standard wide-angle Pade multistep method that uses direct and iterative sparse matrix solvers.
28 citations
TL;DR: A two-way chasing algorithm to reduce a diagonal plus an unsymmetric semi-separable matrix to a bidiagonal one and an algorithm to reducing a diagonalplus an un Symmetric Semi-Separate matrix to an symmetric tridiagonal one are considered.
Abstract: A two-way chasing algorithm to reduce a diagonal plus a symmetric semi-separable matrix to a symmetric tridiagonal one and an algorithm to reduce a diagonal plus an unsymmetric semi-separable matrix to a bidiagonal one are considered. Both algorithms are fast and stable, requiring a computational cost of N2, where N is the order of the considered matrix.
28 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |