Abstract: Interpolation plays an important role in image processing, numerical computation, and engineering technology. Almost all interpolation computation is based on differences and inverse differences. This paper presents the recursive algorithm of modified bivariate block-based Thiele-type blending interpolation to meet the nonexistence of partial inverse differences of blocks. Inspired by the basic thoughts of transformation in linear algebra, this paper studies the information matrix algorithm of bivariate block based Thiele-type blending rational interpolation. The algorithm is simple and easy to compute. Through research, the author presents the interpolation theorems and recursive algorithm and also comes up with the modified bivariate block-based Thiele-type blending rational interpolation, together with its information matrix algorithm, under the nonexistence of block-based partial inverse differences. Finally, a numerical example is introduced to show the effectiveness of the proposed algorithm.

Key words: dual interpolation, information matrix algorithm, block-based partial inverse difference