The topic of this paper is some types of singular behavior of spline approximation methods for one-dimensional singular integral operators which are caused by discontinuities in the coefficients or by non-smooth geometries of the underlying curves. These singularities can be cutted off by a modification of the approximation method which is closely related to the finite or infinite section method for discrete Toeplitz operators. Using Banach algebra techniques, one can derive stability criteria for a large variety of modified methods (including Galerkin, collocation, and qualocation.
Cite this article
Steffen Roch, Spline Approximation Methods Cutting Off Singularities. Z. Anal. Anwend. 13 (1994), no. 2, pp. 329–345DOI 10.4171/ZAA/510