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On Lagrange interpolatory parabolas to $\left | x\right | ^{\alpha }$ at equally spaced nodes

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Abstract.

In this paper we present a generalized quantitative version of a result due to D. L. Berman concerning the exact convergence rate at zero of Lagrange interpolation polynomials to \(\left | x\right | ^{\alpha }\) based on equally spaced nodes in [-1, 1]. The estimates obtained turn out to be best possible.

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  1. Department of Mathematics, University Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria, , , , , , AT

    M. Revers

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  1. M. Revers
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Received: 1.2.1999

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Revers, M. On Lagrange interpolatory parabolas to $\left | x\right | ^{\alpha }$ at equally spaced nodes. Arch. Math. 74, 385–391 (2000). https://doi.org/10.1007/s000130050458

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  • DOI: https://doi.org/10.1007/s000130050458

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