Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1994-06-30
Spline Approximation Methods Cutting Off SingularitiesSteffen Roch (1) Technische Hochschule Darmstadt, Germany
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.
Keywords: Spline approximation methods, singular integral operators, Mellin operators
Roch Steffen: Spline Approximation Methods Cutting Off Singularities. Z. Anal. Anwend. 13 (1994), 329-345. doi: 10.4171/ZAA/510