ALGEBRAIC VERSIONS OF TWO GEOMETRIC METHODS FOR SOLVING SYSTEMS OF LINEAR EQUATIONS

Document Type : Original Article

Authors
Nesa Najafi
Mojtaba Ghasemikamalvand ΒΆ
Department of Mathematics, Lorestan University, Khorramabad, Iran.
10.22034/maco.5.2.10
Abstract
In this article, we obtain algebraic versions of algorithms NGHK and KL (two geometric methods for solving systems
of linear equations), that is, we show that in these two algorithms,
the vector sequences that converge to the solution of the system of
linear equations are located in the row space of the coefficients matrix of system. In the following, we will compare these algorithms
with the Gauss-Seidel method by providing a few examples.
In this article, we obtain algebraic versions of algorithms NGHK and KL (two geometric methods for solving systems
of linear equations), that is, we show that in these two algorithms,
the vector sequences that converge to the solution of the system of
linear equations are located in the row space of the coefficients matrix of system. In the following, we will compare these algorithms
with the Gauss-Seidel method by providing a few examples.

Keywords

Subjects

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Mathematical Analysis and Convex Optimization
Volume 5, Issue 2
December 2025