Interval arithmetic determinant evaluation and its use in testing for a Chebyshev system

Abstract

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