Guaranteed a posteriori error bounds for low-rank tensor approximate solutions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00541908" target="_blank" >RIV/67985840:_____/21:00541908 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/imanum/draa010" target="_blank" >https://doi.org/10.1093/imanum/draa010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imanum/draa010" target="_blank" >10.1093/imanum/draa010</a>
Alternative languages
Result language
angličtina
Original language name
Guaranteed a posteriori error bounds for low-rank tensor approximate solutions
Original language description
We propose a guaranteed and fully computable upper bound on the energy norm of the error in low-rank tensor train (TT) approximate solutions of (possibly) high-dimensional reaction–diffusion problems. The error bound is obtained from Euler–Lagrange equations for a complementary flux reconstruction problem, which are solved in the low-rank TT representation using the block alternating linear scheme. This bound is guaranteed to be above the energy norm of the total error, including the discretization error, the tensor approximation error and the error in the solver of linear algebraic equations, although quadrature errors, in general, can pollute its evaluation. Numerical examples with the Poisson equation and the Schrödinger equation with the Henon–Heiles potential in up to 40 dimensions are presented to illustrate the efficiency of this approach.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IMA Journal of Numerical Analysis
ISSN
0272-4979
e-ISSN
1464-3642
Volume of the periodical
41
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
27
Pages from-to
1240-1266
UT code for WoS article
000651815700014
EID of the result in the Scopus database
2-s2.0-85116905135