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June  2022, 12(2): 293-308. doi: 10.3934/naco.2021006

## Convergence of interval AOR method for linear interval equations

 Department of Mathematics, National Institute of Technology Meghalaya, Shillong, India-793003

* Corresponding author: Manideepa Saha

Received  June 2020 Revised  January 2021 Published  June 2022 Early access  February 2021

A real interval vector/matrix is an array whose entries are real intervals. In this paper, we consider the real linear interval equations $\bf{Ax} = \bf{b}$ with ${{\bf{A}} }$, $\bf{b}$ respectively, denote an interval matrix and an interval vector. The aim of the paper is to study the numerical solution of the linear interval equations for various classes of coefficient interval matrices. In particular, we study the convergence of interval AOR method when the coefficient interval matrix is either interval strictly diagonally dominant matrices, interval $L$-matrices, interval $M$-matrices, or interval $H$-matrices.

Citation: Jahnabi Chakravarty, Ashiho Athikho, Manideepa Saha. Convergence of interval AOR method for linear interval equations. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 293-308. doi: 10.3934/naco.2021006
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Solution set of linear interval equation
Solution set $\sum(\textbf{A},b).$
Solution set $\sum(\textbf{A},b).$
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