The Several Problems In Continued Fration Research

The theory of continued fractions is an old branch of mathematics,its application become more and more wide with the development of science and technology,especially the rational interpolants based on continued fractions.In this paper,the main work include two parts:the application of rational anti-interpolation in numerical optimization based continued fraction and the duality of block-based bivariate rational interpolants.In this paper,based on continued fractions of rational interpolation,we deal with the extreme value problem.This method is simple,easy to programming,the result is better than general iterative method,we can obtain faster convergence speed and higher accuracy.The effectiveness of this method is also verified by numerical examples.In this paper,we further investigate the feature of Block-based bivariate Thiele rational interpolants,acquire the duality of rational interpolants based on the same block form and show some numerical examples.Finally,the validity is also verified.