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: Experimental results show that the simple parallel prefix algorithm is a good algorithm for symmetric, almost symmetric Toeplitz tridiagonal systems and for the compact scheme on high-performance computers.
Abstract: A compact scheme is a discretization scheme that is advantageous in obtaining highly accurate solutions. However, the resulting systems from compact schemes are tridiagonal systems that are difficult to solve efficiently on parallel computers. Considering the almost symmetric Toeplitz structure, a parallel algorithm, simple parallel prefix (SPP), is proposed. The SPP algorithm requires less memory than the conventional LU decomposition and is efficient on parallel machines. It consists of a prefix communication pattern and AXPY operations. Both the computation and the communication can be truncated without degrading the accuracy when the system is diagonally dominant. A formal accuracy study has been conducted to provide a simple truncation formula. Experimental results have been measured on a MasPar MP-1 SIMD machine and on a Cray 2 vector machine. Experimental results show that the simple parallel prefix algorithm is a good algorithm for symmetric, almost symmetric Toeplitz tridiagonal systems and for the compact scheme on high-performance computers.
9 citations
TL;DR: In this paper, the authors generalized the Rayleigh-Schrodinger perturbation formalism to the hamiltonians H = H 0 + λH 1 where the correction H 0 was small and the unperturbed operator H 0 is represented by an infinite tridiagonal matrix.
9 citations
TL;DR: One-step algebraic models with symmetric and positive definite tridiagonal Toeplitz matrices are introduced and their qualitative properties are studied and theoretical results are applied to the numerical solution of parabolic differential equations.
Abstract: One-step algebraic models with symmetric and positive definite (SPD) tridiagonal Toeplitz matrices are introduced and their qualitative properties are studied. Theoretical results are applied to the numerical solution of parabolic differential equations, with illustrations by numerical examples. Possible extensions as well as arising open problems are discussed in concluding remarks.
9 citations
1 Mar 1990
TL;DR: The solver based on the modified Gaussian elimination method fully exploits parallelism and Computation and communication complexities of the proposed algorithm are all shown to be O(n/m).
Abstract: A new tridiagonal Toeplitz linear system (TTLS) solver is proposed. The solver first decomposes an n-dimensional strictly diagonally dominant TTLS equation into a number of m-dimensional subsystems employing a modified Gaussian elimination method. An analytic solution of a continued fraction is obtained to derive the solver. The solver based on the modified Gaussian elimination method fully exploits parallelism. Computation and communication complexities of the proposed algorithm are all shown to be O(n/m).
9 citations
31 May 2001
TL;DR: A framework based on graph theoretic notations is described for the design and analysis of a wide range of parallel tridiagonal matrix algorithms that comprises of three basic types of graph transformation operations: partition, selection, elimination and update.
Abstract: A framework based on graph theoretic notations is described for the design and analysis of a wide range of parallel tridiagonal matrix algorithms. It comprises of three basic types of graph transformation operations: partition, selection, elimination and update. We use the framework to present a unified description of many known parallel algorithms for the solution of tridiagonal systems. We also discuss the use of this framework to design parallel algorithms.
9 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |