Constructive algebraic geometry methods were used to discuss multivariate interpolation problems for which the interpolation nodes are taken from one algebraic manifold and the related theories and algorithms for constructing minimal degree interpolation basis were presented.

We construct the two-dimensional directional orthogonal wavelet through orthogonalizing periodic cardinal interpolatory wavelet which has adjustable-smoothness and is sensitive to the direction,and then perform fast directional wavelet transform.

Solving the Euler equations by wavelet interpolation;

To acquire image with higher resolution without changing the hardware,bilinear interpolation and wavelet interpolation algorithm is analyzed.

This article introduces several interpolation algorithms,the wavelet interpolation in particular.

The interpolating wavelet bases are constructed in order to deal with boundary conditions conveniently, and two-dimensional interpolating wavelet bases in product form are used to construct the generalized field functions of thick plate.

A novel online adaptive repairing method for outliers over data streams,called adaptive interpolating wavelet(AdaptiveIW),is then proposed.

An interpolating wavelet collocation method (IWCM) for adaptive solution of wave propagation in layered media with non-periodic boundary condition is presented.