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Rational interpolation to |x| at the Chebyshev nodes

Published online by Cambridge University Press:  17 April 2009

Lev Brutman  and
Eli Passow
Lev Brutman
Affiliation:
Department of Mathematics and Computer ScienceUniversity of HaifaHaifa 31905Israel e-mail: [email protected]
Eli Passow
Affiliation:
Department of MathematicsTemple UniversityPhiladelphia PA 19122United States of America e-mail: [email protected]
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Abstract

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Recently the authors considered Newman-type rational interpolation to |x| induced by arbitrary sets of interpolation nodes and showed that under mild restrictions on the location of the interpolation nodes, the corresponding sequence of rational interpolants converges to |x|. In the present paper we consider the special case of the Chebyshev nodes which are known to be very efficient for polynomial interpolation. It is shown that, in contrast to the polynomial case, the approximation of |x| induced by rational interpolation at the Chebyshev nodes has the same order as rational interpolation at equidistant points.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 56 , Issue 1 , August 1997 , pp. 81 - 86
Copyright
Copyright © Australian Mathematical Society 1997

References

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