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
1 / 2
Papers
TL;DR: An algorithm for the determination of the eigenvalues of tridiagonal symmetric interval matrices is presented and it only needs twice as many operations as the Sturm algorithm, which is used for real matrices.
Abstract: An algorithm for the determination of the eigenvalues of tridiagonal symmetric interval matrices is presented. The intervals of the eigenvalues are not overestimated, but exactly calculated. The algorithm is an efficient one, because it only needs twice as many operations as the Sturm algorithm, which is used for real matrices. >
9 citations
1 Sep 1990
TL;DR: This work shows how to transform the solution of an n × n tridiagonal system into suffix computations of continued fractions, and introduces a parallel substitution scheme to compute the suffix values.
Abstract: We first show how to transform the solution of an n × n tridiagonal system into suffix computations of continued fractions. Then a parallel substitution scheme is introduced to compute the suffix values. The derived parallel algorithm allows the tridiagonal system to be solved in O(log n) time on an unshuffle network with Θ(n /log n) processors. It is cost-optimal in the sense that processor number times execution time is minimized. Our solver is conceptually simple and easy for implementation.
9 citations
TL;DR: In this paper, an explicit representation with nested sums for the entries of the inverses of general tridiagonal nonsingular matrices is proposed, and its equivalence with other particular representations, based on the combinatorial expressions or the continued fractions is considered.
Abstract: In this note, we propose an explicit representation with the nested sums for the entries of the inverses of general tridiagonal nonsingular matrices. Its equivalence with other particular representations, based on the combinatorial expressions or the continued fractions, is considered. In addition, an analytical representation for the entries of the finite sections of the resolvent of Jacobi matrices, in terms of its related orthogonal polynomials, is observed.
9 citations
TL;DR: The results of Wilkinson on the stability of Gaussian elimination with column pivoting are generalized.
Abstract: The results of Wilkinson on the stability of Gaussian elimination with column pivoting are generalized.
9 citations
TL;DR: An explicit derivation of a tridiagonal matrix form for the almost Mathieu operator (Harper's equation) is obtained via conjugation with a reflection operator, valid for all rational values of the rotation parameter as discussed by the authors.
Abstract: An explicit derivation of a tridiagonal matrix form for the almost Mathieu operator (Harper's equation) is obtained via conjugation with a reflection operator, valid for all rational values of the rotation parameter. The difference between even and odd values of the denominator is highlighted. This tridiagonal form is useful for numerical eigenvalue computations; some Matlab code is included.
9 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |