Abstract
This chapter highlights the error in trigonometric interpolation to nonperiodic smooth functions on arbitrary intervals of length less than 2π. The trigonometric analogs for polynomial interpolation to a smooth function g are studied at m points x1, x2… xm. The t-differences can be used to give a Newton form for the trigonometric Hermite interpolation polynomial and they can be computed recursively in a difference scheme. The chapter also discusses trigonometric B-splines, trigonometric interpolation I, and trigonometric interpolation II.
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