On simultaneous factoring of a polynomial

Abstract

The well-known Durand-Kerner method for simultaneous rootfinding for a polynomial was generalized by Grau for simultaneous factoring of a polynomial. In this note the third order method of Maehly, Ehrlich and Aberth for simultaneous rootfinding of polynomial zeros is generalized for simultaneous factoring of a polynomial in total and single-step mode. The second aim of this note is the algebraic description of the mentioned algorithms such that the euklidian algorithm is applied for evaluating the algorithms. Numerical examples are included.

Keywords:

• Polynomial zeros
• iteration algorithm
• Newton-Raphson's method
• Newton-Jacobi's method
• simultaneous methods
• single step methods
• factorization of polynomials