Approximation operators for matrix-valued functions based on matrix decompositions

TL;DR

This paper introduces a novel approximation operator for matrix-valued functions that leverages matrix decompositions to improve approximation accuracy and analyze properties, extending existing methods.

Contribution

It presents a new approximation method based on matrix decompositions, offering enhanced structure exploitation and analytical tools for matrix-valued functions.

Findings

Demonstrates improved approximation accuracy on example matrices

Provides theoretical analysis tools for the generated matrix functions

Extends existing approximation methods using matrix decompositions

Abstract

Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the structure of the matrices in the samples set, and based on decomposition theorems. We introduce our approach in detail and discuss its advantages using a few examples. In addition, we provide basic tools for analyzing properties of the matrix functions generated by our approximation operators.