A new multi-step ABS model to solve full row rank linear systems
Subject Areas : Statistics
Mahmoud
Paripour
1
(Department of Computer Engineering and Information Technology, Hamadan University of Technology, Hamadan, Iran)
Esmaeil
Babolian
2
(Faculty of Mathematical and Computer Sciences, Kharazmi University, Karaj, Iran)
Leila
Asadbeigi
3
(Faculty of Basic Sciences, Department of Mathematics, Hamadan Branch, Islamic Azad University, Hamadan, Iran)
Keywords: روشهای ABS, روشهای ABS سهگامی, دستگاههای معادلات خطی تمام رتبه سطری, فشردگی فضای محاسبات, روشهای ABS دوگامی,
Abstract :
ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress than corresponding Huang’s method. Also, these ABS-type models need less number of multiplications for a square system. In this paper, in order to economize and compress required space, we present a new three-step ABS procedure that is terminated in at most [((m+2))/3] steps. Computational complexity is considerable up to those corresponding Huang’s method and initial two-step ABS approaches. we present a new three-step ABS procedure that is terminated in at most [((m+2))/3] steps. Computational complexity is considerable up to those corresponding Huang’s method and initial two-step ABS approaches.
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