On the degree of convergence of piecewise polynomial approximation on optimal meshes

Author:
H. G. Burchard

Journal:
Trans. Amer. Math. Soc. **234** (1977), 531-559

MSC:
Primary 41A15

DOI:
https://doi.org/10.1090/S0002-9947-1977-0481758-4

MathSciNet review:
0481758

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Abstract: The degree of convergence of best approximation by piecewise polynomial and spline functions of fixed degree is analyzed via certain *F*-spaces (introduced for this purpose in [2]). We obtain two *o*-results and use pairs of inequalities of Bernstein- and Jackson-type to prove several direct and converse theorems. For *f* in we define a derivative in , which agrees with for smooth *f*, and prove several properties of .

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DOI:
https://doi.org/10.1090/S0002-9947-1977-0481758-4

Article copyright:
© Copyright 1977
American Mathematical Society