Stieltjes polynomials and Lagrange interpolation

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Stieltjes polynomials and Lagrange interpolation

Bounds are proved for the Stieltjes polynomial En+1, and lower bounds are proved for the distances of consecutive zeros of the Stieltjes polynomials and the Legendre polynomials Pn. This sharpens a known interlacing result of Szegö. As a byproduct, bounds are obtained for the Geronimus polynomials Gn. Applying these results, convergence theorems are proved for the Lagrange interpolation process...

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ژورنال

عنوان ژورنال: Mathematics of Computation

سال: 1997

ISSN: 0025-5718

DOI: 10.1090/s0025-5718-97-00808-9