On (0,1,2) interpolation in uniform metric
József Szabados,A. K. Varma +1 more
- Vol. 109, Iss: 4, pp 975-979
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TLDR
In this paper, it was shown that for any given matrix of nodes there exists a continuous function for which the Lagrange interpolation polynomial L n [f,x], generated by the nth row of the matrix, does not tend uniformly to f(x).Abstract:
From the well known theorem of G. Faber it follows that for any given matrix of nodes there exists a continuous function for which the Lagrange interpolation polynomial L n [f,x], generated by the nth row of the matrix, does not tend uniformly to f(x). We shall provide analogous results for the related operator H n,3 [f,x] as defined belowread more
Citations
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Journal ArticleDOI
On the order of magnitude of fundamental polynomials of hermite interpolation
Journal ArticleDOI
On Hermite Interpolation
TL;DR: More general and stronger estimations of bounds for the fundamental functions of Hermite interpolation of higher order on an arbitrary system of nodes are given in this article, based on this result conditions for convergence of the Hermite- Fejer-type interpolation and Grunwald type theorems are essentially simplified and improved.
Journal ArticleDOI
On higher order Hermite-Fejér interpolation in weightedLp-metric
József Szabados,A. K. Varma +1 more
Journal ArticleDOI
On Hermite-Fejér type interpolation on the Chebyshev nodes
TL;DR: A precise estimate for the magnitude of the approximation error is developed and a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the Chebyshev nodes to obtain a convergent rational interpolatory process is demonstrated.
References
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On Interpolation I
Paul Erdös,Paul Turán +1 more
TL;DR: This nutshell answers the following question: if the authors know output values at some finite number of input values — a “look up table” — how can they estimate the output for inputs “in between” the input values of their look-up table?