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: In this article, it was shown that for each n ⩾ 2 there is a nilpotent n × n tridiagonal matrix satisfying (a) the super-diagonal is positive, (b) the sub-diagonal is negative, and (c) the diagonal is zero except that the ( 1, 1 ) position is negative and the ( n, n ) positions are positive.
5 citations
1 Feb 1989
TL;DR: A fast vector algorithm which solves tridiagonal linear equations by an optimum synthesis of the inherently recursive Gaussian elimination and the parallel though complex cyclic reduction and a maximum vector speedup of 13 is revealed.
Abstract: We present a fast vector algorithm which solves tridiagonal linear equations by an optimum synthesis of the inherently recursive Gaussian elimination and the parallel though complex cyclic reduction. The idea is to perform an incomplete cyclic reduction to bring the dimension of the tridiagonal system efficiently below a characteristic size n ∗ and then to solve the remaining system by Gaussian elimination. Extensive numerical experiments on the CYBER 205 and the CRAY X-MP computers reveal a maximum vector speedup of 13 and prove n ∗ to reflect the architecture of the vector computer. The performance is further enhanced when a feq right-hand sides are treated simultaneously.
5 citations
TL;DR: It is proved convergence for the basic LR algorithm on a real unreduced tridiagonal matrix with a one-point spectrum—the Jordan form is one big Jordan block.
Abstract: We prove convergence for the basic LR algorithm on a real unreduced tridiagonal matrix with a one-point spectrum—the Jordan form is one big Jordan block. First we develop properties of eigenvector matrices. We also show how to deal with the singular case.
5 citations
TL;DR: In this article, the authors considered element-wise perturbations of non-symmetric tridiagonal M-matrices and obtained bounds on the perturbation so that the non-negative inverse persists.
5 citations
1 Jan 2001
TL;DR: In this article, an explicit inversion formula for tridiagonal coefficient matrices using Yamamoto-Ikebe's inversion was given, which is the only known formula for such matrices.
Abstract: Discretizing two-point boundary value problems on an interval by finite difference method, we obtain a certain type of tridiagonal coefficient matrices. In this paper we give an explicit inversion formula for such tridiagonal matrices using Yamamoto-Ikebe’s inversion formula.
5 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |