On adaptive cross approximation

Adaptive cross approximation (ACA) is a popular techniques to construct low-rank approximations from entry-wise queries of a matrix or function. In the first part of this talk, we present a non-asymptotic a priori error analysis of ACA. This allows us to identify a nontrivial class of matrices for which the error of ACA is guaranteed to stay close to the best low-rank approximation error. In the second part of this talk, we present a novel extension of ACA to parameter-dependent matrices, as they arise - for example - in uncertainty quantification. This also yields a new variant of ACA for tensors of third order. If time permits, the modified ACA is compared with Riemannian optimizaton techniques. This talk is based on joint work with Alice Cortinovis, Stefano Massei, and others.