Vol. 51, No. 2, 1974

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Sharpened polynomial approximation

Alan Greenwell Law and Ann L. McKerracher

Vol. 51 (1974), No. 2, 491–494

In 1951, W. Wolibner showed that a real continuous function on a closed interval can be uniformly approximated by a polynomial which interpolates at prescribed points and which has a uniform norm agreeing with the function’s. This fit can be sharpened to include matching of some relative extrema as well. The paper characterizes functions that permit Simultaneous Approximation and Interpolation which is Norm-Preserving and Extrema-Matching over the entire interval except, perhaps, for a subset of arbitrarily-small diameter.

Mathematical Subject Classification 2000
Primary: 41A10
Received: 1 February 1973
Published: 1 April 1974
Alan Greenwell Law
Ann L. McKerracher