|
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. E-mail:
uwamusi2000@yahoo.com.
Accepted 14 November, 2011. |
|
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. |
