L. Johnson

Jan 13, 1968

Citations

0

Influential Citations

5

Citations

Journal

Mathematics of Computation

Abstract

For/ continuous and real on [0, 1], let ||/|| = max |/(a;)|, x G [0, 1]. In this journal, Moursund [3] proved Theorem 1. Letf be twice differentiable on [0, 1]. Among all polynomials h(x) of degree n or less, let p(x) be the one that minimizes: max \\\h — f\\, \\h' — f'\\\. If q(x) is another such minimizing polynomial, then q' = p'. Let /• denote the ith derivative of /. Moursund's result can be extended to : Theorem 2. Let f be (k + l)-times differentiable on [0, 1]. Among all polynomials hix) of degree n or less, let pix) be the one that minimizes:

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