Journal Article10.1007/BF02253462
A parallel algorithm for solving special tridiagonal systems on ring networks
4
TL;DR: A fast parallel algorithm for solving the special tridiagonal systems, which includes the skew-symmetric andtridiagonal-Toeplitz systems, is presented, Employing the diagonally dominant property, the parallel solver does need only local communications between adjacent processors on a ring network.
read more
Abstract: The solution of special linear, circulant-tridiagonal systems is considered. In this paper, a fast parallel algorithm for solving the special tridiagonal systems, which includes the skew-symmetric and tridiagonal-Toeplitz systems, is presented. Employing the diagonally dominant property, our parallel solver does need only local communications between adjacent processors on a ring network. An error analysis is also given. On the nCUBE/2E multiprocessors, some experimental results demonstrate the good performance of our stable parallel solver.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Parallel B-Spline Surface Fitting on Mesh-Connected Computers
Kuo-Liang Chung,Wen-Ming Yan +1 more
TL;DR: This paper presents a novel approximateO(n/p)-time parallel B-spline curve fitting algorithm for finding the correspondingncontrol points that interpolate thosendata points on a linear array processor withpprocessors, wherep?n.
9
Vectorized algorithms for solving special tridiagonal systems
Kuo-Liang Chung,Wen-Ming Yan +1 more
TL;DR: Two fast vectorized algorithms for solving special tridiagonal systems that employ the matrix perturbation technique and have many computational advantages on vector supercomputer are presented.
3
A scalable communicationless parallel algorithm for tri-diagonal toeplitz systems
R. E. Shaw,L. E. Garey,Jeffrey Mark Mcnally +2 more
- 01 Jan 2003
TL;DR: Improvements to the previously mentioned methods, as well as a new parallel method for solving tri-diagonal Toeplitz systems of linear equations on multiple processors, which removes the need for correction vectors.
2
•Journal Article
Algorithms for Special Tridiagonal Systems.
TL;DR: In this paper, the authors considered the problem of solving symmetric diagonally dominant tridiagonal systems of linear equations with constant diagonals using the Fourier method and the cyclic reduction method of Hockney and Evans.
1
References
•Book
Numerical solution of partial differential equations : finite difference methods
Gordon Dennis Smith
- 01 Jan 1978
TL;DR: In this article, the standard finite difference methods of parabolic, hyperbolic, and elliptic equations are discussed, together with the concomitant theoretical work on consistency, stability, and convergence.
2.3K
•Book
LINPACK Users' Guide
Jack Dongarra,Cleve B. Moler,J. R. Bunch,G. W. Stewart +3 more
- 01 Jan 1987
TL;DR: General matrices Band matrices positive definite matrices Positive definite band matrices Symmetric Indefinite Matrices Triangular matrices Tridiagonal matrices The Cholesky decomposition The QR decomposition up to and including the singular value decomposition is studied.
1.7K
Topological properties of hypercubes
Y. Saad,M.H. Schultz +1 more
TL;DR: The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing and propose a theoretical characterization of the n-cube as a graph.
1.4K
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
TL;DR: This work has developed a direct method of solution involving Fourier analysis which can solve Poisson''s equation in a square region covered by a 48 x 48 mesh in 0.9 seconds on the IBM 7090.
715
Related Papers (5)
Ibrahim N. Hajj,Stig Skelboe +1 more
- 01 Sep 1990
Fabio Reale
- 01 Dec 1990
Thiab R. Taha,Peiqing Jiang +1 more
- 31 Dec 1993