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A fast non-polynomial interpolation is proposed in this paper for functionswith logarithmic singularities. It can be executed fast with the discretecosine transform. Based on this interpolation, a new quadrature is proposed fora kind of logarithmically singular integrals. The interpolation and integrationerrors are also analyzed. Numerical examples of the interpolation andintegration are shown to validate the efficiency of the proposed newinterpolation and the new quadrature.

Fast non-polynomial interpolation and integration for functions with logarithmic singularities