Algebraic solving of interval non-square matrix equations in the form 𝑨 [𝑿]=[𝑩]

Subject Areas : Statistics

Rahele Nuraei ¹ , Mojtaba Ghanbari ²

1 -
2 - Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran.

Received: 2021-10-14 Accepted : 2022-06-01 Published : 2024-01-18

Keywords: حساب بازه‌ایی, معادلات ماتریسی بازه‌ایی, عدد بازه‌ایی, حل جبری,

Abstract :

One of the most widely used equations in some scientific branches is matrix equations. In this paper, a special class of these equations namely the interval matrix equations in the form A [X]=[B] and in its general form (square and non-square) are investigated. Two simple methods for algebraic solving of these equations are presented. In the first proposed method by using the interval arithmetic, an interval matrix equation is transformed into a crisp matrix equation with a much larger dimension. Also, based on the second proposed method and by using some presented concepts, an interval matrix equation is transformed into two crisp matrix equations with the same initial dimension. A necessary and sufficient condition for the existence of a unique algebraic solution is presented in a special case. In addition, to show the ability and efficiency of these two methods, numerical examples are provided in cases where the equation has unique algebraic solution or infinite algebraic solution.

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