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Volume 3, Issue 3
A Posteriori Error Estimator for Spectral Approximations of Completely Continuous Operators

Y. Yang & Q. Huang

Int. J. Numer. Anal. Mod., 3 (2006), pp. 361-370.

Published online: 2006-03

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  • Abstract

In this paper, we study numerical approximations of eigenvalues when using projection method for spectral approximations of completely continuous operators. We improve the theory depending on the ascent of $T - \mu$ and provide a new approach for error estimate, which depends only on the ascent of $T_h - \mu_h$. Applying this estimator to the integral operator eigenvalue problems, we obtain asymptotically exact indicators. Numerical experiments are provided to support our theoretical conclusions.

  • Keywords

completely continuous operators, projection method, eigenvalues, a posteriori error estimates.

  • AMS Subject Headings

65N25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-3-361, author = {Y. Yang and Q. Huang}, title = {A Posteriori Error Estimator for Spectral Approximations of Completely Continuous Operators}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {3}, pages = {361--370}, abstract = {

In this paper, we study numerical approximations of eigenvalues when using projection method for spectral approximations of completely continuous operators. We improve the theory depending on the ascent of $T - \mu$ and provide a new approach for error estimate, which depends only on the ascent of $T_h - \mu_h$. Applying this estimator to the integral operator eigenvalue problems, we obtain asymptotically exact indicators. Numerical experiments are provided to support our theoretical conclusions.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/907.html} }
TY - JOUR T1 - A Posteriori Error Estimator for Spectral Approximations of Completely Continuous Operators AU - Y. Yang & Q. Huang JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 361 EP - 370 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/907.html KW - completely continuous operators, projection method, eigenvalues, a posteriori error estimates. AB -

In this paper, we study numerical approximations of eigenvalues when using projection method for spectral approximations of completely continuous operators. We improve the theory depending on the ascent of $T - \mu$ and provide a new approach for error estimate, which depends only on the ascent of $T_h - \mu_h$. Applying this estimator to the integral operator eigenvalue problems, we obtain asymptotically exact indicators. Numerical experiments are provided to support our theoretical conclusions.

Y. Yang and Q. Huang. (2006). A Posteriori Error Estimator for Spectral Approximations of Completely Continuous Operators. International Journal of Numerical Analysis and Modeling. 3 (3). 361-370. doi:
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