A New Unified , Localized , and Efficient Approach to Integral Equations

Overview A new approach is presented for solving integral equations. It is a fundamental computational and theoretical advance that provides a unified, fully localized, and computationally efficient solution in closed-form that is useful in both symbolic and numeric computations. The approach is naturally suited for fine-grain parallel implementation. In practical problems such as shift-variant image deblurring, the new approach offers significant computational speed-up in comparison with standard current techniques. Since Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) can be reformulated as integral equations by taking boundary conditions into account, the new approach is also relevant to solving ODEs and PDEs. It is also useful in image/signal filtering, and the analysis and modeling of linear and non-linear systems and processes, in engineering and applied sciences.