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Extended reduced rank two Abaffian update schemes in the ABS-type methods
, Article Applied Mathematics and Computation ; Volume 185, Issue 1 , 2007 , Pages 255-265 ; 00963003 (ISSN) ; Mahdavi Amiri, N ; Peyghami, M. R ; Sharif University of Technology
2007
Abstract
The ABS methods, introduced by Abaffy, Broyden and Spedicato, are direct iteration methods for solving a linear system where the ith iterate satisfies the first i equations, therefore a system of m equations is solved in at most m steps. Recently, we have presented a new approach to devise a class of ABS-type methods for solving full row rank systems [K. Amini, N. Mahdavi-Amiri, M. R. Peyghami, ABS-type methods for solving full row rank linear systems using a new rank two update, Bulletin of the Australian Mathematical Society 69 (2004) 17-31], the ith iterate of which solves the first 2i equations. Here, to reduce the space and computation time, we use a new extended rank two update formula...