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Rounding Error Analysis of Interval Algorithms
Author(s) -
Stummel F.
Publication year - 1984
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19840640807
Subject(s) - rounding , interval (graph theory) , interval arithmetic , mathematics , round off error , midpoint , algorithm , linearization , polynomial , fraction (chemistry) , nonlinear system , mathematical analysis , computer science , combinatorics , geometry , bounded function , chemistry , physics , organic chemistry , quantum mechanics , operating system
Using the linearization method, a rounding error analysis of interval algorithms is established. It is shown that the interval midpoints and radii are approximate solutions of real evaluation algorithms and of certain linear systems uniquely associated to each interval algorithm. In addition, interval data and interval rounding condition numbers are defined which yield optimal bounds of the possible magnitude of the interval radii. These concepts and tools are applied to the following numerical examples: evaluation of a polynomial, continued fraction expansion, summation procedure, and Cramer's rule for two linear equations in two unknowns.