Open AccessModified Nguyen and Revol’s method for solution set of linear interval system based on Rohn’s method without interval data inputs.
Author(s) -
Stephen Ehidiamhen Uwamusi
Publication year - 2015
Publication title -
deleted journal
Language(s) - English
Resource type - Journals
ISSN - 1596-6208
DOI - 10.4314/gjmas.v12i1.17
Subject(s) - interval (graph theory) , interval arithmetic , mathematics , linear system , bounding overwatch , residual , set (abstract data type) , algorithm , factorization , solution set , term (time) , computer science , mathematical analysis , artificial intelligence , combinatorics , bounded function , programming language , physics , quantum mechanics
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