Low-Rank Approximations for Parametric Non-Symmetric Elliptic Problems

In this study, we obtained low-rank approximations for the solution of parametric non-symmetric elliptic partial differential equations. We proved existence optimal approximation subspaces that minimize error between and an on subspace, with respect to mean quadratic norm associated any preset in space solutions. Using a tensorized decomposition, built expansion approximating solutions summands finite-dimensional strong convergence truncated expansion. For rank-one approximations, similar PGD expansion, linear power iteration method compute modes series data small enough. presented some numerical results good agreement theoretical analysis.