Geodesic
Optimization of Rational Approximations by Continued Fractions
Serdica Journal of Computing, Tome 1 (2007) no. 4, pp. 433-442

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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.
Keywords: C-XSC, Continued Fractions, Error Bounds, Special Functions 
@article{SJC_2007_1_4_a3,
     author = {Blomquist, Frithjof},
     title = {Optimization of {Rational} {Approximations} by {Continued} {Fractions}},
     journal = {Serdica Journal of Computing},
     pages = {433--442},
     publisher = {mathdoc},
     volume = {1},
     number = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SJC_2007_1_4_a3/}
}
TY  - JOUR
AU  - Blomquist, Frithjof
TI  - Optimization of Rational Approximations by Continued Fractions
JO  - Serdica Journal of Computing
PY  - 2007
SP  - 433
EP  - 442
VL  - 1
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJC_2007_1_4_a3/
LA  - en
ID  - SJC_2007_1_4_a3
ER  - 
%0 Journal Article
%A Blomquist, Frithjof
%T Optimization of Rational Approximations by Continued Fractions
%J Serdica Journal of Computing
%D 2007
%P 433-442
%V 1
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJC_2007_1_4_a3/
%G en
%F SJC_2007_1_4_a3
Blomquist, Frithjof. Optimization of Rational Approximations by Continued Fractions. Serdica Journal of Computing, Tome 1 (2007) no. 4, pp. 433-442. http://geodesic.mathdoc.fr/item/SJC_2007_1_4_a3/