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

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.