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
16 Dec 2015
TL;DR: A stable parallel algorithm based on WZ factorization for solving diagonally dominant tridiagonal linear system of algebraic equations, using divide and conquer approach is presented.
Abstract: In this work, we present a stable parallel algorithm based on WZ factorization for solving diagonally dominant tridiagonal linear system of algebraic equations, using divide and conquer approach. Existence results are given and the backward error analysis of the method is presented. Numerical stability of the algorithm is proved. The given parallel algorithm for diagonally dominant tridiagonal linear systems is compared with the Truncated SPIKE version of the SPIKE algorithm [12].
3 citations
Posted Content•
TL;DR: Gaussian elimination algorithms have an application in building a public-key cryptosystem, and it is demonstrated that they have an applications in solving the word problem.
Abstract: Gaussian elimination is used in special linear groups to solve the word problem. In this paper, we extend Gaussian elimination to unitary groups. These algorithms have an application in building a public-key cryptosystem, we demonstrate that.
3 citations
TL;DR: In this article, a generalized SOR method with multiple relaxation parameters was considered for solving a linear system of equations and it was shown that if a pair of parameter values is computed from the pivots of the Gaussian elimination applied to the system, then the spectral radius of the iterative matrix is reduced to zero.
Abstract: Recently, a generalized SOR method with multiple relaxation parameters were considered for solving a linear system of equations and it was shown that if a pair of parameter values is computed from the pivots of the Gaussian elimination applied to the system, then the spectral radius of the iterative matrix is reduced to zero. A proper choice of orderings and starting vectors for the iteration were also proposed.
3 citations
3 citations
TL;DR: Two algorithms for computing the inverse factors of general tridiagonal and pentadiagonal matrices are obtained and these algorithms are used for computing a block ILU preconditioner for the blocktridiagonal linear system of equations.
Abstract: Two algorithms for computing the inverse factors of general tridiagonal and pentadiagonal matrices are obtained. Then, these algorithms are used for computing a block ILU preconditioner for the block tridiagonal linear system of equations. Some numerical results are given to show the robustness and efficiency of the preconditioner. The performance of the proposed preconditioner is compared with a recently proposed method.
3 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |