On some open problems of P. Turán concerning Birkhoff interpolation

Varma, A. K.

doi:10.1090/S0002-9947-1982-0675080-2

On some open problems of P. Turán concerning Birkhoff interpolation
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by A. K. Varma PDF

Trans. Amer. Math. Soc. 274 (1982), 797-808 Request permission

Abstract:

In 1974 P. Turán (see [6]) raised many interesting open problems in Approximation Theory some of which are on Birkhoff Interpolation. The object of this paper is to answer some of these problems (XXXVI-XXXIX). We obtain some new quadrature formulas where function values and second derivatives are only prescribed on the zeros of \[ {\pi _n}(x) = {c_n}\int _{ - 1}^x {{P_{n - 1}}(t) dt} \], ${P_n}(x)$ being Legendre polynomial of degree $n$.

References

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Birkhoff interpolation

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