Fully computable a posteriori error bounds for eigenfunctions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00561025" target="_blank" >RIV/67985840:_____/22:00561025 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00211-022-01304-0" target="_blank" >https://doi.org/10.1007/s00211-022-01304-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00211-022-01304-0" target="_blank" >10.1007/s00211-022-01304-0</a>
Alternative languages
Result language
angličtina
Original language name
Fully computable a posteriori error bounds for eigenfunctions
Original language description
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple eigenvalues, under the settings of target eigenvalue problems. Algorithm I is based on the Rayleigh quotient and the min-max principle that characterizes the eigenvalue problems. The formula for the error estimate provided by Algorithm I is easy to compute and applies to problems with limited information of Rayleigh quotients. Algorithm II, as an extension of the Davis–Kahan method, takes advantage of the dual formulation of differential operators along with the Prager–Synge technique and provides greatly improved accuracy of the estimate, especially for the finite element approximations of eigenfunctions. Numerical examples of eigenvalue problems of matrices and the Laplace operators over convex and non-convex domains illustrate the efficiency of the proposed algorithms.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA20-01074S" target="_blank" >GA20-01074S: Adaptive methods for the numerical solution of partial differential equations: analysis, error estimates and iterative solvers</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Numerische Mathematik
ISSN
0029-599X
e-ISSN
0945-3245
Volume of the periodical
152
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
39
Pages from-to
183-221
UT code for WoS article
000824307900001
EID of the result in the Scopus database
2-s2.0-85134293670