6 problems

Let $\mathcal M$ be the parameter set, let $H$ be the coarse-mesh size, let $ell$ be the oversampling parameter, and let … be the localization error indicator for $mu\in\mathcal M$…

Time-step consistency conjecture. The lack of convergence of $\textbf{OG-3x}$, $\textbf{SS-OG-1x}$ and $\textbf{SS-OG-3x}$ in the previous experiments is due to the time step size…

Let $H(\lambda)$ have lowest eigenvalue $E(\lambda)$ with corresponding eigenvector $\phi(\lambda)$. For each nonnegative integer $\ell$, let $\mathcal{P}^\ell$ be the orthogonal p…

Consider reduced-order approximations of seismic wave solutions, with accuracy measured by the convergence rate of the approximation error as the reduced basis is enriched. High-fr…

The reduced-order model (ROM) is constructed using proper orthogonal decomposition and reduced-basis methods for seismic wave propagation, with seismograms as the observed outputs…

Let $F$ be a subset of a Banach space $\mathcal{X}$, let $d_n(F,\mathcal{X})$ denote its $n$-width, and let $Lambda_n$ be the Lebesgue constant of the generalized empirical interpo…