A class of strongly stable operator approximations

Mario Ahues

doi:10.1017/S0334270000005518

Abstract

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We show the strongly stable convergence of some non-collectively-compact approximations of compact operators. Special attention is devoted to Anselone's singularity subtraction discretization of certain singular integral operators. Numerical experiments are provided.

References

[1]Anselone, P. M., Collectively Compact Operator Approximation Theory (Prentice-Hall, Englewood Cliffs, New Jersey, 1971).Google Scholar

[2]Anselone, P. M., “Singularity Subtraction in the Numerical Solution of Integral Equations”, J. Austral. Math. Soc. Ser. B 22 (1981), 408–418.Google Scholar

[3]Chatelin, F., Spectral Approximation of Linear Operators (Academic Press, New York, 1983).Google Scholar

Crossref Citations

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Ahues, Mario 1989. A note on strong stability of finite element approximations. Applied Mathematics Letters, Vol. 2, Issue. 2, p. 179.

Ahues, Mario Arancibia, Sara and Telias, Mauricio 1990. Rayleigh-schrödinger series for defective spectral elements of compact operators in banach spaces. Numerical Functional Analysis and Optimization, Vol. 11, Issue. 9-10, p. 839.

Bouldin, Richard 1990. Operator approximations with stable elgenvalues. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 49, Issue. 2, p. 250.

Ahues, Mario and Largillier, Alain 1990. Rayleigh-schrödinger series for defective spectral elements of compact operators in banach spaces. Numerical Functional Analysis and Optimization, Vol. 11, Issue. 9-10, p. 851.

Nair, M. Thamban 1992. On strongly stable approximations. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 52, Issue. 2, p. 251.

Largillier, Alain and Levet, Mauricio 1993. A note on a collectively compact approximation for weakly singular integral operators. Applied Mathematics Letters, Vol. 6, Issue. 4, p. 87.

Ahues, Mario Largillier, Alain and Limaye, Balmohan 1993. A note on iterative refinement schemes for Sylvester operator equations. Applied Mathematics Letters, Vol. 6, Issue. 4, p. 83.

Ahues, M. and Hocine, F. 1994. A note on spectral approximation of linear operations. Applied Mathematics Letters, Vol. 7, Issue. 2, p. 63.

Levet, M. and Telias, M. 1994. Advances in Optimization and Numerical Analysis. p. 261.

Largillier, A. 1994. A note on the gap convergence. Applied Mathematics Letters, Vol. 7, Issue. 2, p. 67.

Ahues, Mario and Largillier, Alain 1995. A variant of the fixed tangent method for spectral computations on integral operators. Numerical Functional Analysis and Optimization, Vol. 16, Issue. 1-2, p. 1.

Dang, P.T.D. 1995. A note on finite-element spectral computations for integro-differential operators. Applied Mathematics Letters, Vol. 8, Issue. 4, p. 43.

Alam, Rafikul 1998. On Spectral Approximation of Linear Operators. Journal of Mathematical Analysis and Applications, Vol. 226, Issue. 1, p. 229.

Ahues, Mario Largillier, Alain and Titaud, Olivier 2001. THE ROLES OF A WEAK SINGULARITY AND THE GRID UNIFORMITY IN RELATIVE ERROR BOUNDS. Numerical Functional Analysis and Optimization, Vol. 22, Issue. 7-8, p. 789.

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Hadji, Soufiane and Zguitti, Hassane 2024. Local spectral properties and $$\nu $$-convergence. Rendiconti del Circolo Matematico di Palermo Series 2,

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A class of strongly stable operator approximations

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