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Towards a Vector Field Based Approach to the Proper Generalized Decomposition (PGD)
- Source :
- Mathematics, Vol 9, Iss 1, p 34 (2020)
- Publication Year :
- 2020
- Publisher :
- MDPI AG, 2020.
-
Abstract
- A novel algorithm called the Proper Generalized Decomposition (PGD) is widely used by the engineering community to compute the solution of high dimensional problems. However, it is well-known that the bottleneck of its practical implementation focuses on the computation of the so-called best rank-one approximation. Motivated by this fact, we are going to discuss some of the geometrical aspects of the best rank-one approximation procedure. More precisely, our main result is to construct explicitly a vector field over a low-dimensional vector space and to prove that we can identify its stationary points with the critical points of the best rank-one optimization problem. To obtain this result, we endow the set of tensors with fixed rank-one with an explicit geometric structure.
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 9
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.0d82797e7b3f4ce5a3b064b6cd3c66be
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/math9010034