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Emphasis of Coefficients on the Convergence Rate of Fixed Point Iterative Algorithm in Banach Space
Naveen Kumar
Pages: 1-18 | First Published: 05 Oct 2022
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Abstract
This paper deals with the fixed point iterative schemes that are being utilized to solve the systems of nonlinear equations in various fields and spaces. The convergence speed of iterative processes is highly focused, calculated and compared with various original methods to check the efficiency of these methods towards its optimal solution. The effect on the speed of convergence by the coefficients included in these iterative algorithms are investigated and analyzed in this manuscript. Moreover, the results on the convergence rate of various fixed point iterative schemes are supported by comparing the convergence rate of these iterative plans using the methodology of interchanging the coefficients of these algorithms. The convergence behaviour of these iterative processes is also shown graphically. In a nut shell, the comparison analysis shows that the coefficients involved in such type of schemes may vary the convergence rate of the schemes towards their fixed points.
Keyword: Banach Space, Contractive Mapping, Convergence Rate, Fixed Point Iterations, Fixed Point.
 

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