Verified bounds for nonlinear systems via Hansen-Sengupta method
Stephen Ehidiamhen Uwamusi · International Journal of the Physical Sciences · 2009
Efficient numerical validation of solution to nonlinear systems of equations using the Hansen-Sengupta method is the main focus of our studies. An extremely fast method due to (Uwamusi, 2007) is used to accelerate basic characteristic convergence of the method. This is not surprising because the midpoints and radii of the convergent interval vectors obtained are coupled sequence via the inclusion isotonicity of interval arithmetic which satisfied the filter net condition of a fixed point operator. We compare our results with those obtained using traditional real floating point of Newton method. The emphasis is on the rigor of the bounds. Key words: Nonlinear systems, Hansen-Sengupta method, Newton method, circular complex arithmetic MSC (2000) 65G(20), 65G(30).