Karhunen-Loéve decomposition of isotropic Gaussian random fields using a tensor approximation of autocovariance kernel

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F18%3A10239977" target="_blank" >RIV/61989100:27240/18:10239977 - isvavai.cz</a>
Alternative codes found
RIV/68145535:_____/18:00495896 RIV/61989100:27740/18:10239977
Result on the web
<a href="http://doi.org/10.1007/978-3-319-97136-0_14" target="_blank" >http://doi.org/10.1007/978-3-319-97136-0_14</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-97136-0_14" target="_blank" >10.1007/978-3-319-97136-0_14</a>

Result language
angličtina
Original language name
Karhunen-Loéve decomposition of isotropic Gaussian random fields using a tensor approximation of autocovariance kernel
Original language description
Applications of random fields typically require a generation of random samples or their decomposition. In this contribution, we focus on the decomposition of the isotropic Gaussian random fields on a two or three-dimensional domain. The preferred tool for the decomposition of the random field is the Karhunen-Loéve expansion. The Karhunen-Loéve expansion can be approximated using the Galerkin method, where we encounter two main problems. First, the calculation of each element of the Galerkin matrix is expensive because it requires an accurate evaluation of multi-dimensional integral. The second problem consists of the memory requirements, originating from the density of the matrix. We propose a method that overcomes both problems. We use a tensor-structured approximation of the autocovariance kernel, which allows its separable representation. This leads to the representation of the matrix as a sum of Kronecker products of matrices related to the one-dimensional problem, which significantly reduces the storage requirements. Moreover, this representation dramatically reduces the computation cost, as we only calculate two-dimensional integrals. (C) Springer International Publishing AG, part of Springer Nature 2018.
Czech name
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Czech description
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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Volume 11087
ISBN
978-3-319-97135-3
ISSN
0302-9743
e-ISSN
1611-3349
Number of pages
15
Pages from-to
188-202
Publisher name
Springer
Place of publication
Cham
Event location
Karolinka
Event date
May 22, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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