Adaptive piecewise Poly-Sinc methods for function approximation

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We propose a new method of adaptive piecewise function approximation based on Sinc points. The adaptive method is a Lagrange interpolation scheme which utilizes Poly-Sinc interpolation to reach a preset level of accuracy for the approximation. We prove the exponential convergence of our algorithm. We derive an a priori error estimate for our adaptive method and show its exponential convergence. We use a statistical approach for partition refinement. The adaptive greedy piecewise Poly-Sinc algorithm is validated on continuous, singular, and piecewise functions. We demonstrate that Runge's phenomenon can be handled within a given accuracy goal.