On uniform convergence of approximation methods for operator equations of the second kind |
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Authors: | M. Thamban Nair |
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Affiliation: | Department of Mathematics , Goa University , Goa, 403 202, India |
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Abstract: | Schock (1985) has considered the convergence properties of various Galerkin-like methods for the approximate solution of the operator equation of the second kind x - Tx = y, where T is a bounded linear operator on a Banach space X, and x and y belong to X, and proved that the classical Galerkin method and in certain cases, the iterated Galerkin method are arbitrarily slowly convergent whereas the Kantororich method studied by him is uniformly convergent. It is the purpose of this paper to introduce a general class of approximations methods for x - Tx = y which includes the well-known methods of projection and the quadrature methods, and to characterize its uniform convergence, so that an arbitrarily slowly convergent method can be modified to obtain a uniformly convergent method. |
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Keywords: | Metric regularity Pseudo-Lipschitz multivalued functions Partial tangent cone Tangential approximations Sufficient optimality conditions Tangent approximations |
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