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, an algorithm for the inverse of a general tridiagonal matrix is presented, which is then generalized to deal with general tridagonal matrices without any restriction, indicating low computational complexity of the proposed algorithm.
Abstract: An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.
16 citations
1 Jan 1993
TL;DR: In this paper, the authors describe the first distributed memory implementation of the split-merge algorithm, an eigenvalue solver for symmetric tridiagonal matrices that uses Laguerre's iteration and exploits the separation property in order to create independent subtasks.
Abstract: Abstract Both massively parallel computers and clusters of workstations are considered promising platforms for numerical scientific computing. This paper describes the first distributed-memory implementation of the split-merge algorithm, an eigenvalue solver for symmetric tridiagonal matrices that uses Laguerre's iteration and exploits the separation property in order to create independent subtasks. Implementations of the split-merge algorithm on both an nCUBE-2 hypercube and a cluster of Sun Spare-10 workstations are described, with emphasis on load balancing, communication overhead, and interaction with other user processes. A performance study demonstrates the advantage of the new algorithm over a parallelization of the well-known bisection algorithm. A comparison of the performance of the nCUBE-2 and cluster implementations supports the claim that workstation clusters offer a cost-effective alternative to massively parallel computers for certain scientific applications.
16 citations
TL;DR: In this paper, a numerical analysis of comparison of two configurations to improve heat and mass transfer by the evaporation of two-component liquid film in a vertical channel under mixed convection is presented.
16 citations
TL;DR: A method will be presented which will allow for problems of the above nature to be split into two separate systems which can be solved in parallel, and then combined and corrected to obtain a solution to the original system.
Abstract: In 1994, Yan and Chung produced a fast algorithm for solving a diagonally dominant symmetric Toeplitz tridiagonal system of linear equations Ax = b. In this work a method will be presented which will allow for problems of the above nature to be split into two separate systems which can be solved in parallel, and then combined and corrected to obtain a solution to the original system. An error analysis will be provided along with example cases and time comparison results.
16 citations
21 Jun 1998
TL;DR: This paper shows how the symmetric eigenproblem, which is the computationally most demanding part of numerous scientific and industrial applications, can be solved much more efficiently than by using algorithms currently implemented in Lapack routines.
Abstract: This paper shows how the symmetric eigenproblem, which is the computationally most demanding part of numerous scientific and industrial applications, can be solved much more efficiently than by using algorithms currently implemented in Lapack routines.
16 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |