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
1 Jan 1988
Journal Article•
TL;DR: A new parallel iterative procedure is used to solve arbitrary tridiagonal equations by using the orthogonal projection method, greedy method and partition strategy method, and a new proof of convergence of the algorithm is given.
Abstract: In the rapid development of high-performance parallel computing technology today, the demand of science and engineering numerical calculation is higher and higher. In the numerical calculations, the final solution is converted into the calculation of large-scale system of linear equations. This article focuses on parallel algorithm of tridiagonal equations. Firstly, introduce the current solving tridiagonal linear equations on parallel algorithms: direct solution and the iterative solution. Direct solution, the algorithm is rich, the program is easy to implement, but the amount of calculation is too large, and most of the algorithms for the requirement of the coefficient matrix is relatively high. Iterative solution is more suitable for nonzero elements, especially the iteration solution combination with Krylov subspace. Then, by using the orthogonal projection method, greedy method and partition strategy method, a new parallel iterative procedure is used to solve arbitrary tridiagonal equations. Finally, give a new proof of convergence of the algorithm.
TL;DR: The general expression of the lth power for one type of tridiagonal matrices of order n = 2p + 1 (p ∈ N, p ⩾ 2) is derived.
1 Oct 1988
TL;DR: The author describes an algorithm for computing the characteristic polynomial of a tridiagonal matrix which consists in the application of the divide-and-conquer technique to the evaluation of a three-term recurrence relation.
Abstract: The author describes an algorithm for computing the characteristic polynomial of a tridiagonal matrix. It is quite general and consists in the application of the divide-and-conquer technique to the evaluation of a three-term recurrence relation. The algorithm developed requires O(n log/sup 2/n) arithmetic operations as compared to the classical algorithm that requires O(n/sup 2/) arithmetic operations. >
16 Dec 2006
TL;DR: The experimental results show that only the algorithms that take into account the heterogeneity of the system when balancing the workload obtain optimum performance, justifying the need of implementing specific load balancing techniques for heterogeneous parallel computers.
Abstract: Computation of the eigenvalues of a symmetric tridiagonal matrix is a problem of great relevance. Many linear algebra libraries provide subroutines for solving it. But none of them is oriented to be executed in heterogeneous distributed memory multicomputers. In this work we focus on this kind of platforms. Two different load balancing schemes are presented and implemented. The experimental results show that only the algorithms that take into account the heterogeneity of the system when balancing the workload obtain optimum performance. This fact justifies the need of implementing specific load balancing techniques for heterogeneous parallel computers.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |