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SIA:l.1 J. '1'~IER. '-\:-;,>.L VoL 18. :\0. 5. Octot-er 1981
 

Summary: SIA:l.1 J. '1'~IER. '-\:-;,>.L
VoL 18. :\0. 5. Octot-er 1981
E 1981 Society for lndustrial and Applied Mathematics
0036-1429/81: 1805-0009 501.00 0
ON THE EVALUATION OF RATIONAL FUNCTIONS IN INTERVAL
ARITHMETIC*
G. ALEFELD7 AND J. G. ROKNEt
Abstract. We discuss some new expressions for rational functions for which the Hausdorff distance
between the range over a given interval and the interval arithmetic evaluation has the order of the square
of the width of the given interval.
1. Preliminaries and introduction. Let there be given a real-valued rational
function of the real variable x,
f( ) =g(X)=L~=oayxY
x ,"5 y'
h(x) ':"y=o byx
and a compact interval X = [Xl, X2].If g(X) and heX) denote the interval arithmetic
evaluation of one of the infinitely many equivalent representations of g and h (for
example, by using Horner's method) and if 0 eh (X), then
(l)
(2) f(x) EfeX) := g(X)

  

Source: Alefeld, Götz - Institut für Angewandte und Numerische Mathematik & Fakultät für Mathematik, Universität Karlsruhe

 

Collections: Mathematics