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ABS-type methods for solving full row rank linear systems using a new rank two update

Published online by Cambridge University Press:  17 April 2009

K. Amini ,
N. Mahdavi-Amiri  and
M. R. Peyghami
K. Amini
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, e-mail: Amini@mehr.sharif.edu, Nezamm@sina.sharif.edu, Peyghami@mehr.sharif.edu
N. Mahdavi-Amiri
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, e-mail: Amini@mehr.sharif.edu, Nezamm@sina.sharif.edu, Peyghami@mehr.sharif.edu
M. R. Peyghami
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, e-mail: Amini@mehr.sharif.edu, Nezamm@sina.sharif.edu, Peyghami@mehr.sharif.edu
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ABS mthods are direct iteration methods for solving linear systems where the i-th iterate satisfies the first i equations, and therefore a system on m equations is solved in at most m ABS steps. In this paper, using a new rank two update of the Abaffian matrix, we introduce a class of ABS-type methods for solving full row rank linear equations, where the i-th iterate solves the first 2i equations. So, termination is achieved in at most ⌊(m + 1)/2⌋ steps. We also show how to decrease the dimension of the Abaffian matrix by choosing appropriate parameters.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 1 , August 2004 , pp. 17 - 34
Copyright
Copyright © Australian Mathematical Society 2004

References

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