Solution of Preconditioned System of Interval Linear Equations

Nirmala, T.; Ganesan, K.

doi:10.37896/gor33.02/248

Cited by 1 publication

(1 citation statement)

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“…In [22,27] methods have been published to find tolerable solutions. Also, some methods have been developed to obtain controllable solutions [14,28] and exact solutions [12,14,[29][30][31] of interval linear systems.…”

Section: ×=mentioning

confidence: 99%

Two Iterative Methods for Solving Linear Interval Systems

Siahlooei

Fazeli

2018

Applied Computational Intelligence and Soft Computing

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Conjugate gradient is an iterative method that solves a linear system Ax=b, where A is a positive definite matrix. We present this new iterative method for solving linear interval systems Ãx̃=b̃, where Ã is a diagonally dominant interval matrix, as defined in this paper. Our method is based on conjugate gradient algorithm in the context view of interval numbers. Numerical experiments show that the new interval modified conjugate gradient method minimizes the norm of the difference of Ãx̃ and b̃ at every step while the norm is sufficiently small. In addition, we present another iterative method that solves Ãx̃=b̃, where Ã is a diagonally dominant interval matrix. This method, using the idea of steepest descent, finds exact solution x̃ for linear interval systems, where Ãx̃=b̃; we present a proof that indicates that this iterative method is convergent. Also, our numerical experiments illustrate the efficiency of the proposed methods.

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