Geometric Interpretation of Best Rational Approximation and Simple Continued Fractions

2021 ◽  
Vol 3 (5) ◽  
pp. 71-73
Author(s):  
William Li
Keyword(s):  
Rational Approximation ◽  
Continued Fractions ◽  
Geometric Interpretation ◽  
Best Rational Approximation

On Padé and Best Rational Approximation

1983 ◽  
Vol 26 (1) ◽  
pp. 50-57 ◽  
Author(s):  
Peter B. Borwein
Keyword(s):  
Rational Approximation ◽  
Analytic Functions ◽  
Unit Disc ◽  
Padé Approximants ◽  
Main Diagonal ◽  
Rational Approximations ◽  
Pade Approximants ◽  
Best Rational Approximation

AbstractIt is reasonable to expect that, under suitable conditions, Padé approximants should provide nearly optimal rational approximations to analytic functions in the unit disc. This is shown to be the case for ez in the sense that main diagonal Padé approximants are shown to converge as expeditiously as best uniform approximants. Some more general but less precise related results are discussed.

Adaptive Fourier decompositions and rational approximations, part I: Theory

2014 ◽  
Vol 12 (05) ◽  
pp. 1461008 ◽  
Author(s):  
Tao Qian
Keyword(s):  
Rational Approximation ◽  
One Dimension ◽  
Rational Approximations ◽  
Different Types ◽  
Best Rational Approximation

In this paper, we will give a survey on adaptive Fourier decompositions (AFDs) in one- and multi-dimensions. Theoretical formulations of three different types of AFDs in one-dimension, viz., Core AFD, Cyclic AFD in conjunction with best rational approximation and Unwending AFD are provided.

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