A root-finding algorithm based on Newton's method

Research paper by Kaj Madsen

Indexed on: 01 Mar '73Published on: 01 Mar '73Published in: BIT Numerical Mathematics


This note is a short description of a procedure searching for the zero of least modulus of a given polynomial. Further details may be found in [8].The method is based on Newton's formula, and the main problem is to find an approximation to the zero, close enough to make Newton's method converge. We solve this problem iteratively, making use of the information Newton's formula gives about the direction of steepest descent. In this way we obtain a sequence of points giving decreasing function values. When a certain condition is fulfilled, securing convergence of Newton's method, this is used directly.With very few modifications the procedure can be used to find a zero of an arbitrary analytic functionf:C →C.