Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products
In this paper, we present new Tensor extrapolation methods as generalizations of well known vector, matrix and block extrapolation methods such as polynomial extrapolation methods or <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics>...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1298 |
| _version_ | 1797560088503779328 |
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| author | Alaa El Ichi Khalide Jbilou Rachid Sadaka |
| author_facet | Alaa El Ichi Khalide Jbilou Rachid Sadaka |
| author_sort | Alaa El Ichi |
| collection | DOAJ |
| description | In this paper, we present new Tensor extrapolation methods as generalizations of well known vector, matrix and block extrapolation methods such as polynomial extrapolation methods or <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>-type algorithms. We will define new tensor products that will be used to introduce global tensor extrapolation methods. We discuss the application of these methods to the solution of linear and non linear tensor systems of equations and propose an efficient implementation of these methods via the global-QR decomposition. |
| first_indexed | 2024-03-10T17:54:29Z |
| format | Article |
| id | doaj.art-0c80521a26da4a9b94eafe412d0ad87d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T17:54:29Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0c80521a26da4a9b94eafe412d0ad87d2023-11-20T09:13:09ZengMDPI AGMathematics2227-73902020-08-0188129810.3390/math8081298Tensor Global Extrapolation Methods Using the n-Mode and the Einstein ProductsAlaa El Ichi0Khalide Jbilou1Rachid Sadaka2LABMIA-SI, Department of Mathematics, University Mohammed V Rabat, Rabat 10000, MoroccoDepartment of Mathematics LMPA, 50 rue F. Buisson, ULCO, 62100 Calais, FranceLABMIA-SI, Department of Mathematics, University Mohammed V Rabat, Rabat 10000, MoroccoIn this paper, we present new Tensor extrapolation methods as generalizations of well known vector, matrix and block extrapolation methods such as polynomial extrapolation methods or <inline-formula><math display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>-type algorithms. We will define new tensor products that will be used to introduce global tensor extrapolation methods. We discuss the application of these methods to the solution of linear and non linear tensor systems of equations and propose an efficient implementation of these methods via the global-QR decomposition.https://www.mdpi.com/2227-7390/8/8/1298Einstein productKrylov subspacessequence transformationtensor extrapolation |
| spellingShingle | Alaa El Ichi Khalide Jbilou Rachid Sadaka Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products Mathematics Einstein product Krylov subspaces sequence transformation tensor extrapolation |
| title | Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products |
| title_full | Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products |
| title_fullStr | Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products |
| title_full_unstemmed | Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products |
| title_short | Tensor Global Extrapolation Methods Using the n-Mode and the Einstein Products |
| title_sort | tensor global extrapolation methods using the n mode and the einstein products |
| topic | Einstein product Krylov subspaces sequence transformation tensor extrapolation |
| url | https://www.mdpi.com/2227-7390/8/8/1298 |
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