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Generalized order star theory

Part II: Short Communications

Part of the Lecture Notes in Mathematics book series (LNM,volume 888)

Abstract

In this paper we generalize the theory of order stars of Wanner, Hairer and Nørsett [14]. We show that there is a geometric relation between the location of the zeros and the poles of a rational approximation to the exponential and the distribution of its interpolation points.

By applying this theory we find that the A-acceptability and the general form of the denominator impose bounds on the number and location of the interpolation points. These bounds are used to characterize the A-acceptability properties of various families of rational approximations to exp(x), in particular to verify a conjecture of Ehle [2] on the order-constrained Chebishev approximations.

Much of the paper is based upon a joint work of the author with M.J.D. Powell [8].

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References

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© 1981 Srpinger-Verlag

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Iserles, A., College, K. (1981). Generalized order star theory. In: de Bruin, M.G., van Rossum, H. (eds) Padé Approximation and its Applications Amsterdam 1980. Lecture Notes in Mathematics, vol 888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095589

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  • DOI: https://doi.org/10.1007/BFb0095589

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11154-2

  • Online ISBN: 978-3-540-38606-3

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