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
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Papers
TL;DR: A theoretical bound to the basis of this exponential decay of the off-diagonal blocks of the matrix sequences generated by the Cyclic Reduction algorithm is provided together with a tool for its estimation based on a rational interpolation problem.
20 citations
7 Jun 1988
TL;DR: In this paper, the authors examined two approaches for reducing parallel sparse matrix solution time: the first based on pivot ordering algorithms for Gaussian elimination, and the second based on relaxation algorithms.
Abstract: The authors examine two approaches for reducing parallel sparse matrix solution time: the first based on pivot ordering algorithms for Gaussian elimination, and the second based on relaxation algorithms A pivot ordering algorithm is presented which increases the parallelism of Gaussian elimination compared to the commonly used Markowitz method The minimum number of parallel steps for the solution of a tridiagonal matrix is derived, and it is shown that this optimum is nearly achieved by the ordering heuristics which attempt to maximize parallelism Also presented is an optimality result about Gauss-Jacobi over Gauss-Seidel relaxation on parallel processors >
20 citations
TL;DR: In this article, the authors consider the problem of finding a real symmetric tridiagonal matrix whose graph is a given tree, motivated both by known results and recent work on multiplicities and interlacing equalities.
20 citations
TL;DR: In this article, a finite element finite difference method for solving three-dimensional heat transport equations in a double-layered thin film with microscale thickness was developed, using a preconditioned Richardson iteration, so that only two block tridiagonal linear systems with unknowns at the interface are solved for each iteration.
Abstract: W e develop a finite element?finite difference method for solving three-dimensional heat transport equations in a double-layered thin film with microscale thickness. The implicit scheme is solved by using a preconditioned Richardson iteration, so that only two block tridiagonal linear systems with unknowns at the interface are solved for each iteration. W e then apply a parallel Gaussian elimination procedure to solve these two block tridiagonal linear systems and develop a domain decomposition algorithm for thermal analysis of the double-layered thin film. Numerical results for thermal analysis of a gold layer on a chromium padding layer are obtained.
19 citations
TL;DR: An efficient algorithm for solving the tridiagonal quasi-Toeplitz linear systems is proposed, which takes more floating-point operations (FLOPS) than the L U decomposition method, but needs less memory storage and data transmission and is about twice faster than theL U decompose method.
19 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |