A mixed EIM-SVD tensor decomposition for bivariate functions

Abstract

In this paper we present a mixed EIM-SVD tensor decomposition for bivariate functions. This method is composed, as its name suggests, of two main steps. The first one, provides an approximate representation of a function $f$ in separate form by the use of a Tensor Empirical Interpolation Method (TEIM). The second phase consists in applying the Singular Value Decomposition (SVD) with low-rank truncation to the separate form of $f$ resulting from the first phase. Error estimates of the developed TEIM as well as truncated SVD decomposition are derived. Numerical experiments confirm that the decomposition techniques are efficient in terms of stability and accuracy.