On Computational Review of the Block Schaeffer’s Iteration Formula for Strongly Pseudocontractive Maps of the System of Linear Equations

Abstract

This work reviews the background concepts of the Block Schaeffer’s fixed point iteration for- mula, states
and proves its associated theorems before applying the method in the solution of a given system of linear
equation, the aim of which is to computationally confirm that the traditional Block Schaeffer’s iteration
formula is strongly Pseudo-contractive on convergence. Again this research seeks to computationally
reaffirm that the choice of any initial guess closer to the solution for an iteration formula converges faster
to the solution. The obviousness of this is reflected in the main result highlighted in our computation which
showed that a slight ad- justment in the initial guess becoming x¯∗ = x¯0 ± x¯0 10−1 ; x¯0 ̸ = ¯0 produces
faster convergence automatically, no matter how close x¯0 is to the solution, x∗.