An optimal ball algorithm for fixed point equations

Abstract

Based on a principle of successively minimizing the ball containing the solution set, a new ball algorithm is developed for solving the fixed point equation x = Tx, with T a contractive operator. It is shown that this algorithm is optimal in computational efficiency among all known ball methods for the given problem. Numerical examples are provided to support the conclusion.

Keywords:

• Ball iteration
• Region contraction algorithm
• Dahlquist constant
• Geometric estimator

AMS(M0S) Subject Classification:

• 65J15
• 65G10

C.R Categories:

• G.1.5