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

100%

Regińska T.

Mathematica Applicanda

|

1987

|

tom 16

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nr 30

PL

.

EN

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.

2

Approximate solving of ill posed problems

100%

Regińska T.

Mathematica Applicanda

|

1989

|

tom 17

|

nr 31

PL

Praca ma charakter przeglądowy. Celem pracy jest wyjaśnienie, w jakim sensie można mówić o rozwiązywaniu zadania źle postawionego i pokazanie, że stosując odpowiednią metodę udaje się zadanie to rozsądnie rozwiązywać również w przypadku danych wyjściowych obarczonych błędem. W pracy omówiono metodę regularyzacji i pewne sposoby konstrukcji operatorów regularyzujących występujących w tej metodzie. Na przykładzie równania całkowego Fredholma I rodzaju pokazano metodę wyznaczania rozwiązania przybliżonego.

EN

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.

3

Function representation in wavelet base

100%

Regińska T.

Mathematica Applicanda

|

1995

|

tom 24

|

nr 38

PL

.

EN

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.

4

Review: J. Stoer; Introdution to numeric methods, vol. I; J. Stoer, R. Bulirsch; Introdution to numeric methods, vol. II

100%

Regińska T.

Mathematica Applicanda

|

1983

|

tom 11

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nr 22

PL

Artykuł nie zawiera streszczenia

EN

The article contains no abstract

5

Approximation of eigenvalues of nonselfadjoint problems on an infinite interval

100%

Regińska T.

Mathematica Applicanda

|

1979

|

tom 7

|

nr 14

PL

W pracy badane są zagadnienia własne Lu=a u. Dowodzi się, iż wartości własne tego zagadnienia są aproksymowane przez wartości własne pewnych zagadnień własnych na przedziałach skończonych.

EN

The author treats the problem of approximation of the eigenvalues of the nonselfadjoint problem Lu=λu, u(0)=0, u∈L2(0,∞), where L=−d2/dt2+p(x), domL={u∈L2(0,∞):du/dt continuous, d2u/dt2∈L2(0,∞), u(0)=0}. The same question for a selfadjoint problem was answered in the author's recent paper.

6

On stability of outer inverses

100%

Regińska T.

Mathematica Applicanda

|

1985

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tom 13

|

nr 25

PL

.

EN

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.

7

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

100%

Regińska T.

Mathematica Applicanda

|

1978

|

tom 6

|

nr 13

PL

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).

EN

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.

8

On a certain algorithm of eigenvalue localization for normal operators

64%

Moszyński K., Regińska T.

Banach Center Publications

|

1990

|

tom 24

|

nr 1

533-549

9

Eigenvalue approximation

63%

Regińska T.

Banach Center Publications

|

1984

|

tom 13

|

nr 1

559-573

Ograniczanie wyników

7 Mathematica Applicanda

2 Banach Center Publications

9 Regińska T.

1 Moszyński K.

1 1995

1 1990

1 1989

1 1987

1 1985

1 1984

1 1983

1 1979

1 1978

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

Approximate solving of ill posed problems

Function representation in wavelet base

Review: J. Stoer; Introdution to numeric methods, vol. I; J. Stoer, R. Bulirsch; Introdution to numeric methods, vol. II

Approximation of eigenvalues of nonselfadjoint problems on an infinite interval

On stability of outer inverses

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

On a certain algorithm of eigenvalue localization for normal operators

Eigenvalue approximation