On Local Approximation Properties of L2-Projection on Spline-Subspaces†

作者：Johannes M. Nitsche, A. H. Schatz · 发表于：Applicable Analysis · 年份：1972 · DOI：10.1080/00036817208839035 · 被引用次数：37 · 研究领域：Advanced Numerical Methods in Computational Mathematics、Advanced Numerical Analysis Techniques、Advanced Mathematical Modeling in Engineering

For L2 approximations in an intervel I and a sequences by'local approximation properties' is meant whether a high regularity of the approximated function in i'will give a corresponding small error in the l2sence for proper subintervals I" of I'. Whereas this is not so for the Fourier-sums, it holds true for projections on subspaces fulfilling certain approximability conditions which are typical for splines.