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 1993
TL;DR: The Euler and Navier Stokes equations are discretized and numerically solved on distributed memory parallel processors for airfoil geometries and the Thomas Algorithm is used to solve the block tridiagonal matrices that result from the implicit AD1 scheme.
Abstract: The Euler and Navier Stokes equations are discretized and numerically solved on distributed memory parallel processors for airfoil geometries. The spatial derivatives are evaluated to second order accuracy with upwind differencing and the equations are solved implicitly using AD1 factorization. The Thomas Algorithm is used to solve the block tridiagonal matrices that result from the implicit AD1 scheme. The recursion inherent in this method is dealt with by transposing the domain amongst the processors so that there is no communication required in order to solve the tridiagonals once the transpose is done. A couple of transpose schemes were considered and results are presented for the most efficient. Very good times are achieved for realistic problems when run on a coarse to medium grain machine. The method is compared with other parallel schemes. The code was developed and run on an nCUBE/2 and also run on a Thinking Machines CM-5 for a performance comparison and to illustrate portability of the code. *Graduate Assistant tPrincipal St& Scientist, Associate Fellow AIAA $Associate Professor, Senior Member AIAA 5 Graduate Assistant, Member AIAA Vcopyright 1993 @by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
1 citations
1 Feb 1989
TL;DR: The results show that the two algorithms are equivalent in terms of error complexity measures, and the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.
Abstract: A novel general approach to round-off error analysis using the error complexity concepts is described. This is applied to the analysis of the Gaussian Elimination and Gauss-Jordan scheme for solving linear equations. The results show that the two algorithms are equivalent in terms of our error complexity measures. Thus the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.
1 citations
TL;DR: A fast algorithm is given for the inverse of the class of tridiagonal period matrices, which has much important applications in computational mathematics, physics, image processing and recognition, missile system design, nonlinear kinetics, economics and biology etc.
Abstract: The Tridiagonal period Matrices, as an important tool, have much important applications ( such as in computational mathematics, physics, image processing and recognition, missile system design, nonlinear kinetics, economics and biology etc). In this paper, we give a fast algorithm for the inverse of the class of tridiagonal period matrices .
1 citations
15 Aug 2001
TL;DR: A new parallel solver for nonsymmetric tridiagonal matrices is proposed, which is an improvement over the dissection method, and the LU decomposition of the whole matrix with partial pivoting can be done in parallel.
Abstract: We propose a new parallel solver for nonsymmetric tridiagonal matrices, which is an improvement over the dissection method. The conventional dissection method is difficult to apply to a general nonsymmetric tridiagonal matrix, because the independence of decomposition operations in each subdomain is lost when pivoting is introduced. In our algorithm, due to the reordering of the nodes adjacent to the boundary nodes, the independence of decomposition operations in each subdomain is guaranteed even when partial pivoting is introduced. Thus, the LU decomposition of the whole matrix with partial pivoting can be done in parallel. We evaluated our algorithm on 1 node of the SR8000/F1 (a shared-memory parallel computer with 8 processors) and obtained speedup of 5.5 times compared with the conventional sequential tridiagonal solver with pivoting, when computing the LU decomposition of a nonsymmetric tridiagonal matrix of order 8000.
1 citations
TL;DR: A method for computing the positive integer powers of the anti-tridiagonal matrix corresponding to these matrices corresponding to two certain types of tridiagonal matrices of arbitrary order is presented.
Abstract: In this paper, we firstly derive a general expression for the entries of the
m
th (
m
∈
ℕ
) power for two certain types of tridiagonal matrices of arbitrary order. Secondly, we present a method for computing the positive integer powers of the anti-tridiagonal matrix corresponding to these matrices. Also, we give Maple 18 procedures in order to verify our calculations.
1 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |