Lagrange interpolation on extended generalized Jacobi nodes |
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Authors: | Jürgen Prestin |
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Affiliation: | (1) Fachbereich Mathematik, UniversitÄt Rostock, D-18051 Rostock, Germany |
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Abstract: | We consider theLp-convergence of interpolatory processes for nonsmooth functions. Therefore we use generalizations of the well-known Marcinkiewicz-Zygmund inequality for trigonometric polynomials to the case of algebraic polynomials, extending a result of Y. Xu. Particularly, we obtain the order of convergence for certain Lagrange and quasi-Lagrange interpolatory processes on generalized Jacobi nodes. Our approach enables us also to discuss the influence of additional nodes near the endpoints ±1. |
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