Fast Exact Evaluation of Univariate Kernel Sums

This paper presents new methodology for computationally efficient evaluation of univariate kernel sums. It is shown that a rich class kernels allows exact functions expressed as sum using simple recursions. Given an ordered sample the computational complexity linear in size. Direct applications to estimation denisties and their derivatives shows proposed approach competitive with state-of-the-art. Extensions multivariate problems including independent component analysis spatial smoothing illustrate versatility estimators, highlight efficiency accuracy approach. Multiple image processing, deconvolution; denoising; reconstruction are considered, showing offers very promising potential these fields.