Piecewise trigonometric Hermite interpolation

Based on the symmetric, nonnegative and normalized basis of the trigonometric polynomial space, the piecewise trigonometric Hermite interpolation methods are presented. The Cn−1Cn−1 and Cn continuous piecewise trigonometric Hermite interpolants of degree n are constructed and the interpolation methods are local. The integral and the differential representations of the errors of the trigonometric Hermite interpolants are given. Several examples are supplied to support the practical value of the given interpolation methods.