Cross Approximation

Cross approximation is a technique for efficiently approximating large matrices and tensors by selecting a small subset of their elements to represent the whole. Current research focuses on improving the accuracy and efficiency of cross approximation algorithms, particularly for high-dimensional tensors and in applications like image compression and machine learning. This involves developing novel algorithms, such as greedy maximal volume approaches, and rigorously analyzing approximation errors, especially for tensor train decompositions. These advancements have significant implications for reducing computational costs in various fields, including enabling power-efficient printed electronics for machine learning applications.