International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2569

Full Length Research Paper

Effects of repeatedly used preconditioner on computational accuracy for nonlinear interval system of equations

Stephen Ehidiamhen Uwamusi
Department of Mathematics, Faculty of Physical Sciences, University of Benin, Benin City, Nigeria.
Email: [email protected]

  •  Accepted: 14 November 2011
  •  Published: 09 December 2011

Abstract

 

We discuss Hansen-Sengupta operator in the context of circular interval arithmetic for the algebraic inclusion of zeros of interval nonlinear systems of equations. It was demonstrated by showing the effects of applying repeatedly preconditioners of inverses of the midpoint interval matrices on the well known Trapezoidal Newton method at each iteration cycle wherein, the work of Shokri (2008) was our major tool of investigation. It was shown that the Trapezoidal interval Newton method with inverse midpoint interval matrix as preconditioner is not a H-continuous map and that Baire category failed to hold in the sense of Aguelov et al. (2007). This was more so since it produced from our numerical example, not only overestimated results but, also results that are not finitely bounded which we compare with results computed previously given in Uwamusi.

 

Key words: Interval nonlinear systems of equations, Hansen–Sengupta operator, Trapezoidal Newton method, circular interval arithmetic, H-continuous map.