Accelerated generalized successive overrelaxation method for least squares problems

摘要

In this paper we develop a new iterative method for solving large and sparse least squares problems. We accelerate the generalized successive overrelaxation method. The advantage of this method is that to cover some of difficulties of the well known methods such as GS, SOR and AOR [D. Young, Iterative Solution of Large Linear Systems, Academic Press, New York, London, 1971 [1]; G. Meurant, Computers Solution of Linear Systems Studies in Mathematics and its Applications, vol. 28, Elsevier/North Holland, 1999 [2]], GSOR [C. Li, B. Li, J. Evans, A generalized successive overrelaxation method for least squares problems, BIT 2(2) (1998) 347–355; C. Li, B. Li, J. Evans, Optimum acceleration parameter for the GSOR method, Neural, Parallel and Scientific Computations 7 (1999) 453–462].AGSOR method involved two-parameter. By using AGSOR we can solve large linear systems in ill-condition problems. These ill-posed systems has zeroes block or sparse coefficients matrix, even we can not improve ill-condition by interchanging rows and columns.