Abstract
The paper is a modificationofNguyen and Revol‟s method for the solution set to the linear interval system. The presented methoddoes not require solving Kahan‟s arithmetic which may be a hindrance to that of Nguyen and Revol‟s method as Nguyen and Revol‟s method relies mainly on interval data inputs.Our method under consideration first advances solutionusing real floating point LU Factorization to the real point linear system and then solves a preconditioned residual linear interval system for the error term by incorporating Rohn‟s method which does not make use of interval data inputs wherein, the use of united solution set in the sense of Shary comes in handy as a tool for bounding solution for the linear interval system. Special attention is paid to the regularity of the preconditioned interval matrix. Numerical exampleis used to illustrate the algorithm and remarks are made based on the strength of our findings.KEY WORDS:refinement of solution, linear interval system, Rohn‟s method, Hansen-Bliek-Rohnmethod, preconditioned residual linear interval iteration, kahan‟s arithmetic
Highlights
The paper aims at presenting amodification for the Nguyen and Revol‟smethod,Nguyen and Revol(2011), by using classical LU floating point real arithmetic to advance solution to systems of linear equations and switches to a method due to Rohn (2010a) that is free of interval data inputs,which solves preconditioned residual linear interval system that is guaranteed to enclose all uncertainties as solution set for original linear interval system of equations
We provide the united solution set of the linear interval system (1.1) in the form of equation (1.5) using the procedures we will describe shortly
We noted that(Nguyen and Revol,2011) implanted a kind of Hansen- Sengupta method,Hansen and Sengupta (1981) in their method which they implemented in Moore‟s interval arithmetic
Summary
The paper aims at presenting amodification for the Nguyen and Revol‟smethod,Nguyen and Revol(2011), by using classical LU floating point real arithmetic to advance solution to systems of linear equations and switches to a method due to Rohn (2010a) that is free of interval data inputs,which solves preconditioned residual linear interval system that is guaranteed to enclose all uncertainties as solution set for original linear interval system of equations. We define linear interval systems of equations in the form Ax b , (1.1) Where. The A, A are the lower and upper end points of interval matrix A while b, b are the lower and upper end points for the interval vector b.The Ac is the midpoint for the interval matrix A and bc is defined for the interval vector b. We aim to solve for the unknown interval x IRn in order to obtain the Hull of the solution set.
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