Forward-backward serial iteration methods for simultaneously approximating polynomial zeros

Abstract

Two approaches in realization of iteration methods for simultaneously improving approximations to the polynomial zeros in a serial manner are considered. The new procedure alleviates some unwanted effects which occur in the implementation of iteration methods on sequential computers due to the finite mantissa of floating-point arithmetic and improves R-order of convergence. The accelerated convergence is demonstrated in the examples of most frequently used simultaneous methods.

Keywords:

• Polynomial zeros
• serial iteration methods
• R-order convergence

C.R. Categories:

• 5.15