Luther, U. : Approximation Spaces in the Numerical Analysis of Operator Equations

Author(s):

Luther, U.

Title:

Approximation Spaces in the Numerical Analysis of Operator Equations

Electronic source:

application/postscript

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 16, 2001

Mathematics Subject Classification:

65J10			[ Equations with linear operators ]
41A65			[ Abstract approximation theory ]
45E05			[ Integral equations with kernels of Cauchy type ]

Abstract:

We show that generalized approximation spaces can be used to prove stability and convergence of projection methods for certain types of operator equations in which unbounded operators occur. Besides the convergence, we get also orders of convergence by this approach, even in the case of non-uniformly bounded projections. We give an example in which weighted uniform convergence of the collocation method for an easy Cauchy singular integral equation is studied.

Keywords:

Approximation spaces, Numerical analysis, Cauchy singular integral equations

Language:

English

Publication time:

2 / 2002