# A new algorithm of proper generalized decomposition for parametric symmetric elliptic problems

##### Citations

^{1}, Emmanuelle Abisset

^{2}, Amine Ammar

^{2}, Elías Cueto

^{3}+2 more•Institutions (4)

6 citations

### Cites background from "A new algorithm of proper generaliz..."

...For s ∈ [0, 1] X = x0 + νt, x = sh1(X), For s ∈ [1, 2] X = x0 + νt, x = (s− 1)hg + h1(X), For s ∈ [2, 3] X = x0 + νt, x = (s− 2)h2(X) + hg + h1(X), (44)...

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...s ∈ [0, 1] X = r, x = sh1(X) = sh1(r), s ∈ [1, 2] X = r, x = (s− 1)l + h1(X) = (s− 1)l + h1(r), s ∈ [2, 3] X = r, x = (s− 2)h2(X) + l + h1(X) = (s− 2)h2(r) + l + h1(r), (36)...

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...The interested reader can refer to [2, 7, 11, 20, 23, 25, 26] and the references therein for practical details on the computer implementation of separated representations....

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4 citations

^{1}, Amine Ammar, Jean Louis Duval

^{2}, Francisco Chinesta

^{2}•Institutions (2)

1 citations

^{1}, T. Chacón Rebollo

^{2}, T. Chacón Rebollo

^{1}, M. Gómez Mármol

^{2}•Institutions (2)

##### References

8,491 citations

### "A new algorithm of proper generaliz..." refers background in this paper

...It is referred to as the principal components analysis (PCA) in statistics (see [15, 17, 30]), or called singular value decomposition (SVD) in linear algebra (see [14])....

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8,035 citations

### "A new algorithm of proper generaliz..." refers background in this paper

...It is referred to as the principal components analysis (PCA) in statistics (see [15, 17, 30]) and called singular value decomposition (SVD) in linear algebra (see [14])....

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5,207 citations

### "A new algorithm of proper generaliz..." refers methods in this paper

...The Karhunen--Lo\`eve expansion (KLE) is a widely used tool that provides a reliable procedure for a low-dimensional representation of spatiotemporal signals (see [13, 23])....

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3,177 citations

### "A new algorithm of proper generaliz..." refers background in this paper

...It is named proper orthogonal decomposition (POD) in mechanical computation, where it is also widely used (see [5])....

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536 citations

### "A new algorithm of proper generaliz..." refers background in this paper

...Galerkin-POD strategies are well suited to solving parabolic problems, where the POD basis is obtained from the previous solution of the underlying elliptic operator (see [19, 26])....

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