Stair Matrices and Their Generalizations With Applications to Iterative Methods

SHAO Xin-hui; SHEN Hai-long; LI Chang-jun

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(8): 971-977

SHAO Xin-hui, SHEN Hai-long, LI Chang-jun. Stair Matrices and Their Generalizations With Applications to Iterative Methods[J]. Applied Mathematics and Mechanics, 2006, 27(8): 971-977.

Citation:

SHAO Xin-hui, SHEN Hai-long, LI Chang-jun. Stair Matrices and Their Generalizations With Applications to Iterative Methods[J]. Applied Mathematics and Mechanics, 2006, 27(8): 971-977.

Citation:

SHAO Xin-hui, SHEN Hai-long, LI Chang-jun. Stair Matrices and Their Generalizations With Applications to Iterative Methods[J]. Applied Mathematics and Mechanics, 2006, 27(8): 971-977.

PDF( 289 KB)

Stair Matrices and Their Generalizations With Applications to Iterative Methods

Department of Mathematics, Northeastern University, Shenyang 110004, P. R. China

Received Date: 2004-06-28
Rev Recd Date: 2005-12-27
Publish Date: 2006-08-15

Abstract

Abstract

Stair matrices and their generalizations are introduced.The definitions and some properties of the matrices were first given by Lu Hao.This class of matrices provided bases of matrix splittings for iterative methods.The remarkable feature of iterative methods based on the new class of matrices is that the methods were easily implemented for parallel computation.In particular,a generalization of the accelerated overrelaxation method(GAOR) was introduced.Some theories of the AOR method were extended to the generalized method to include a wide class of matrices.The convergence of the new method was derived for Hermitian positive definite matrices.Finally,some examples are given in order to show the superiority of the new method.
- stair matrices,
- iterative method,
- parallel computation,
- generalization of the AOR method

FullText(HTML)

References(7)

References

[1]	Hadjidimos A.Accelerated overrelaxation method[J].Math Comp,1978,32(2):149—157. doi: 10.1090/S0025-5718-1978-0483340-6
[2]	Varga R S.Matrix Iterative Analysis[M].Englewood Cliffs,NJ:Prentice-Hall,1962,25—132.
[3]	Young D M.Iterative Solution for Large Systems[M].New York:Academic Press,1971，102—145.
[4]	LU Hao.Stair matrices and their generalizations with applications to iterative methods(Ⅰ)—A generalization of the successive overrelaxation method[J]. SIAM J Numer Anal,1999,37(1):1—17. doi: 10.1137/S0036142998343294
[5]	Li C,Li B,Evans D J.A generalized successive overrelaxation method for least squares problems[J].BIT,1998,38(2):347—356. doi: 10.1007/BF02512371
[6]	Varga R S.Extensions of the Successive Overrelaxation Theory With Applications to Finite Element Approximations,in Topics in Numerical Analysis[M].New York:Academic Press,1973,329—343.
[7]	Wild P,Niethammer W.Over- and under-relaxation for linear systems with weakly cyclic Jacobi matrices of index p[J].Linear Algebra Appl,1987,91(1):29—52. doi: 10.1016/0024-3795(87)90058-9