Summary
International Symposium on Nonlinear Theory and its Applications
2005
Session Number:2-1-4
Session:
Number:2-1-4-1
High precision evaluation of nonlinear functions
Siegfried M. Rump,
pp.733-736
Publication Date:2005/10/18
Online ISSN:2188-5079
Summary:
A key to the accurate solution of an illconditioned system of nonlinear equations is the accurate evaluation of the functions is use. For this purpose we present a fast method to emulate quadruple precision for the basic operations as well as for the elementary standard functions. Our methods are based on a recent paper on accurate evaluation of sums and dot products, which in turn uses so-called error-free transformations. We use only double precision floating point operations, and the code contains no branches or access to mantissa or exponent. Hence the algorithms are fast in terms of measured computing time.