Kernel-independent adaptive construction of $\mathcal{H}^2$-matrix approximations

TL;DR

This paper introduces a kernel-independent method for adaptively constructing $\ ext{H}^2$-matrix approximations of non-local operators, improving efficiency and accuracy through new error estimates for adaptive cross approximation.

Contribution

It presents a novel adaptive construction technique for nested bases in $\ ext{H}^2$-matrices and provides new error estimates for ACA with implications for pivoting strategies.

Findings

Effective kernel-independent $\ ext{H}^2$-matrix approximation method.

New error estimates for adaptive cross approximation.

Enhanced understanding of ACA pivoting strategies.

Abstract

A method for the kernel-independent construction of $\mathcal{H}^2$-matrix approximations to non-local operators is proposed. Special attention is paid to the adaptive construction of nested bases. As a side result, new error estimates for adaptive cross approximation~(ACA) are presented which have implications on the pivoting strategy of ACA.