A Low-Rank solution for the first kind Fredholm integral equations based on Deep-QLP decomposition
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In this talk we present a methodology to construct a low-rank solution for the Fredholm integral equations of the first kind with a non-degenerate kernel function. The given Fredholm equation is discretized by using spline function and spline quasi-interpolation based quadrature rule. Since the resulting linear systems can be heavily ill-conditioned, due to the ill-posedness of the original problem, a regularization technique is presented employing a suitable matrix factorization called Deep-QLP. Numerical tests are performed on the famous Phillips and Shaw equations with applications to signal regularization within the framework of improving data quality for AI systems.