SFU MOCAD Seminar: Astrid Herremans

In function approximation, it is standard to assume the availability of an orthonormal basis for computations, ensuring that numerical errors are negligible. However, this assumption is often unmet in practice. For instance, multivariate approximation schemes might use basis functions defined on a tensor-product domain, while the function to be approximated only exists on an irregular subdomain. When restricted to such a subdomain, the basis loses its orthogonality. This work discards the orthogonality assumption, enabling more flexible design of computational methods through the use of non-orthogonal spanning set. To precisely identify when numerical phenomena become significant, we introduce the concept of numerical redundancy. A set of functions is numerically redundant if it spans a lower-dimensional space when analysed numerically rather than analytically. This talk explores the key aspects of computing with such numerically redundant spanning sets, including convergence behaviour, solver requirements, and data efficiency.