2011/06/22 by Antonio Falcó, Falco, Antonio, Anthony Nouy +1 · 1 citation
Computer Science · Engineering · Mathematics · #49M29 #65K10 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Tensor decomposition and applications
paper · doi:10.48550/arxiv.1106.4424
openalex publication_date 2011/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods have been recently introduced for the a priori construction of tensor approximations of the solution of such problems. In this paper, we give a mathematical analysis of a family of progressive and updated Proper Generalized Decompositions for a particular class of problems associated with the minimization of a convex functional over a reflexive tensor Banach space.