Interval Arithmetic Determinant Evaluation
and Its Use in Testing for a Chebyshev System

Two recent papers, one by Hansen and one by
Hansen and R. R. Smith, have shown how Interval 
Arithmetic (I.) can be used effectively to bound errors
in matrix computations.  In the present paper 
a method proposed by Hasen and R. R. Smith is compared
with straightforward use of I. in determinant 
evaluation.  Computational results show the accuracy
and running times that can be expected when using 
I. for determinant evaluation.  An application using
I. determinants in a program to test a set of 
functions to see if they form a Chebyshev system is then presented.

CACM February, 1969

Smith, L. B.

interval arithmetic, range arithmetic, error bounds,
determinant evaluation, Chebyshev system, 
mathematical proof by computer

5.11 5.13 5.14

CA690207 JB February 20, 1978  10:49 AM

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