A mixed EIM-SVD tensor decomposition for bivariate functions

TL;DR

This paper introduces a novel tensor decomposition method combining TEIM and SVD for efficient approximation of bivariate functions, with proven error bounds and validated through numerical experiments.

Contribution

The paper proposes a new mixed EIM-SVD tensor decomposition approach that enhances approximation accuracy and stability for bivariate functions.

Findings

Effective in approximating bivariate functions

Provides error estimates for the decomposition

Numerical results confirm stability and accuracy

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.