Proper generalized decomposition for nonlinear convex problems in tensor Banach spaces

Tensor-based methods are receiving a growing interest in scienti c computing for the numerical solution of problems de ned 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 re exive tensor Banach space. Mathematics Subject Classi cation (2000) 65K10,49M29