# Information Matrix Algorithm of Block-based Bivariate Thiele-Type Rational Interpolation

## Le Zoua,b,c, Liangtu Songb,c, Xiaofeng Wanga, Qiong Zhoub,c,d, Yanping Chena, and Chao Tanga

aDepartment of Computer Science and Technology, Hefei University, Hefei, 230601, China
bInstitute of Intelligent Machines, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei, 230031, China
cUniversity of Science and Technology of China, Hefei, 230026, China
dSchool of Information and Computer, Anhui Agricultural University, Hefei, 230036, China

(Submitted on May 27, 2018; Revised on July 3, 2018; Accepted on August 16, 2018)

## 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.

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