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Convergence of approximation methods for eigenvalue problem for two forms

Teresa Regińska — 1984

Aplikace matematiky

The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space X . We investigate some approximation methods generated by sequences of forms a n and b n defined on a dense subspace of X . The proof of convergence of the methods is based on the theory of the external approximation of eigenvalue problems. The general results are applied to Aronszajn’s method.

Error estimates for external approximation of ordinary differential equations and the superconvergence property

Teresa Regińska — 1988

Aplikace matematiky

A pointwise error estimate and an estimate in norm are obtained for a class of external methods approximating boundary value problems. Dependence of a superconvergence phenomenon on the external approximation method is studied. In this general framework, superconvergence at the knot points for piecewise polynomial external methods is established.

Superconvergence effect in finite element methods for two-point boundary value problems

Teresa Regińska — 1987

Mathematica Applicanda

Approximate methods for solving two-point boundary value problems are considered. The aim of the paper is to explain superconvergence effect in the methods using finite element spaces. The existence of a class of the methods with the superconvergence property is demonstrated. Detailed proofs of superconvergence are presented for the case of the Galerkin method (due to Douglas and Dupont results) and for some example of external method.

Approximate solving of ill posed problems

Teresa Regińska — 1989

Mathematica Applicanda

The paper has a form of review article. The aim of the paper is to explain the meaning of solution of ill posed problem. Moreover, it is shown that by using an appropriate method the ill posed problem can be reasonably solved also in the case of incexact data. The regularization method and, especially, certin methods of constructing regularization operators are discussed. The method of approximate solving of ill posed problems is illustrated by an example of the 1st kind Fredholm equation.

On stability of outer inverses

Teresa Regińska — 1985

Mathematica Applicanda

The paper is concerned with stability properties of bounded outer inverses for bounded operators on Banach spaces. We investigate the effect of perturbations of subspaces generating outer inverses for a given operator. We prove that the convergence of respective gaps between subspaces implies the convergence in the norm of outer inverses generated by these subspaces. The notion of outer inverses is illustrated by an example which gives the form of outer inverses for an arbitrary matrix.

Function representation in wavelet base

Teresa Regińska — 1995

Mathematica Applicanda

The paper concerns wavelet bases in the space L2(M). We give a review of elements of the wavelet theory selected from the point of view of numerical analysis applications. Our purpose is to show properties of a function representation in a wavelet basis, among others, to formulate criteria of global and local function smoothness in terms of its wavelet decomposition coefficients.

Approximation of eigenvalues for a class of differential problems on an infinite interval

Teresa Regińska — 1978

Mathematica Applicanda

The author investigates the problem (1) Lu=λu, u(0)=0, u∈L2(0,∞), where L=d2/dt2+a(t)d/dt+b(t) and domL={u∈L2(0,∞):du/dt absolutely continuous, d2u/dt2∈L2(0,∞), u(0)=0}. She proves that under certain conditions it is possible to approximate the spectrum of (1) by means of the spectrum of a suitable problem of the form −u′′+c(t)u=λu, u(0)=0, u′(n)=α(n)u(n).The review of the paper is available at MR0518666.

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