Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/355

 Title: Optimization of Rational Approximations by Continued Fractions Authors: Blomquist, Frithjof Keywords: C-XSCContinued FractionsError BoundsSpecial Functions Issue Date: 2007 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Journal of Computing, Vol. 1, No 4, (2007), 433p-442p Abstract: To get guaranteed machine enclosures of a special function f(x), an upper bound ε(f) of the relative error is needed, where ε(f) itself depends on the error bounds ε(app); ε(eval) of the approximation and evaluation error respectively. The approximation function g(x) ≈ f(x) is a rational function (Remez algorithm), and with sufficiently high polynomial degrees ε(app) becomes sufficiently small. Evaluating g(x) on the machine produces a rather great ε(eval) because of the division of the two erroneous polynomials. However, ε(eval) can distinctly be decreased, if the rational function g(x) is substituted by an appropriate continued fraction c(x) which in general needs less elementary operations than the original rational function g(x). Numerical examples will illustrate this advantage. Description: The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006. URI: http://hdl.handle.net/10525/355 ISSN: 1312-6555 Appears in Collections: Volume 1 Number 4

Files in This Item:

File Description SizeFormat