On the degree of convergence of piecewise polynomial approximation on optimal meshes
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- by H. G. Burchard PDF
- Trans. Amer. Math. Soc. 234 (1977), 531-559 Request permission
Abstract:
The degree of convergence of best approximation by piecewise polynomial and spline functions of fixed degree is analyzed via certain F-spaces ${\mathbf {N}}_0^{p,n}$ (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 ${\mathbf {N}}_0^{p,n}$ we define a derivative ${D^{n,\sigma }}f$ in ${L^\sigma },\sigma = {(n + {p^{ - 1}})^{ - 1}}$, which agrees with ${D^n}f$ for smooth f, and prove several properties of ${D^{n,\sigma }}$.References
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Additional Information
- © Copyright 1977 American Mathematical Society
- 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