Numerical solution of Fredholm integral equations by the least squares method using QR decomposition

This paper presents a numerical method for solving the second-kind Fredholm integral equations using the least squares approach via QR decomposition. The proposed technique employs Gaussian quadrature for numerical integration and efficiently applies QR decomposition for minimization. This strategy not only simplifies the implementation but also significantly enhances computational performance. A convergence analysis is provided, and several numerical examples demonstrate the accuracy and effectiveness of the method compared to traditional technique.

کلیدواژه ها:

Least squares method ، QR decomposition ، Gauss quadrature rule ، Fredholm integral equations