Numerical analytic continuation of holomorphic functions in
On Some new Inclusion Theorems for the Eigenvalues of Partitioned Matrices.
D'un résultat hilbertien à un principe de comparaison entre spectres. Applications
Optimal uncertainty quantification for legacy data observations of Lipschitz functions
We consider the problem of providing optimal uncertainty quantification (UQ) – and hence rigorous certification – for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter...
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