Abstract
The motivation of the present work is to propose high order iterative methods with a recurrence formula for approximate matrix inversion and provide regularized solution of Fredholm integral equation of first kind with noisy data by an algorithm using the proposed methods. From the given family of methods of orders p = 7,11,15,19 are applied to solve problems of Fredholm integral equation of first kind. From the literature, iterative methods of same orders are used to solve the considered problems and numerical comparisons are shown through tables and figures.
Highlights
Consider the system of linear equationsAx b, A R N1 N1 (1)when, A is nonsingular dense stored matrix
When, A is nonsingular dense stored matrix. Such a system is commonly solved by Gaussian elimination with pivoting and the accuracy of the computed solution depends primarily on the condition number of the matrix A [1]
In order to determine a meaningful approximation of the solution of (1) when the coefficient matrix A is severely ill-conditioned one typically replaces the linear system (1)
Summary
The discretization of the ill-posed problems such as the Fredholm integral equations of first kind with smooth kernel results algebraic linear systems possessing a severely ill-conditioned or singular coefficent matrix and these problems are known as linear discrete ill-posed problems. In these problems the solution is very sensitive to perturbations in the data such as measurement or approximation errors. That is less sensitive to the perturbations of the right-hand side b and the coefficient matrix A (see [2]-[8]) Another approach to find a smooth solution to the ill-conditioned system (1) when A is nonsingular is to use a preconditioner matrix V that approximates A 1. The factorization of hyperpower method of order 7 for computing generalized inverse
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
