14.5.2 Simple-Iteration method

The Simple-Iteration Method, also known as the fixed-point iteration method, offers a fundamental approach to solving equations and systems by iteratively refining initial estimates. Rooted in the principle of successive approximation, the Simple-Iteration Method holds a place of significance across various fields of science and engineering. At its essence, the Simple-Iteration Method transforms complex problems into a sequence of simpler steps. Whether unraveling nonlinear equations, addressing eigenvalue problems, or venturing into the world of optimization, the method's adaptability is a testament to its universal applicability. The heart of the Simple-Iteration Method lies in its ability to sculpt the problem domain into a journey of self-correction.