A combined Remes-differential correction algorithm for rational approximation

Cyclic AFD Algorithm for Best Rational Approximation

We propose a practical algorithm of best rational approximation of a given order to a function in the Hardy H space on the unit circle or on the real line. The type approximation is proved to be equivalent with Blaschke form approximation. The algorithm is called Cyclic AFD as it adaptively selects one parameter during each cycle based on the Maximal Selection Principle used in adaptive Fourier...

A method to obtain the best uniform polynomial approximation for the family of rational function

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

A Comparison of Algorithms for Rational / œ Approximation

Results are reported of a numerical study to compare eight algorithms for obtaining rational L approximations. The algorithms investigated are Loeb's algorithm, the linear inequality algorithm, the Osborne-Watson algorithm, the differential correction algorithms I, II and III, the Remes algorithm and Maehly's algorithm. The results of the study indicate that the Remes algorithm and the differen...

On the Furtwangler algorithm for simultaneous rational approximation

Memetic Electromagnetism Algorithm for Finite Approximation with Rational Bézier Curves

The problem of obtaining a discrete curve approximation to data points appears recurrently in several real-world fields, such as CAD/CAM (construction of car bodies, ship hulls, airplane fuselage), computer graphics and animation, medicine, and many others. Although polynomial blending functions are usually applied to solve this problem, some shapes cannot yet be adequately approximated by usin...