On Methods Derived from Hansen-Patrick Formula for Refining Zeros of Polynominal Equation

Abstract

A one-parameter family of iteration functions as derived by Hansen and Patrick (1977) was studied. The Halley’s method was of particular interest, which was modified by using the Taylor polynomial equation of order two to obtain the well-known Chevbyshev’s iteration formula. Further, using the Laguerre’s disk, two new methods were constructed out of the Chevbyshev’s functional iteration fomula. The obtained methods may, and often will, depend on

the already calculated values.