High-quality image inpainting methods based on nonlinear higher-order partial differential equations have been developed in the last few years. These methods are iterative by nature, with a timeâ€¦ (More)

We propose a linear finite-element discretization of Dirichlet problems for static Hamiltonâ€“Jacobi equations on unstructured triangulations. The discretization is based on simplified localizedâ€¦ (More)

(1) What is lim â†’0 âˆ« 1 xâˆ’1 cos(xâˆ’1 log x) dx? (2) A photon moving at speed 1 in the x-y plane starts at t = 0 at (x, y) = (1/2, 1/10) heading due east. Around every integer lattice point (i, j) inâ€¦ (More)

We consider the approximate solution of selfadjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly nonâ€“uniform tetrahedral mesh which isâ€¦ (More)

Some significant quantities in mathematics and physics are most naturally expressed as the Fredholm determinant of an integral operator, most notably many of the distribution functions in randomâ€¦ (More)

Let u 2 H be the exact solution of a given self{adjoint elliptic boundary value problem, which is approximated by some ~ u 2 S, S being a suitable nite element space. EEcient and reliable aâ€¦ (More)

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analyticallyâ€¦ (More)

We give a short, operator-theoretic proof of the asymptotic independence of the minimal and maximal eigenvalue of the nÃ— n Gaussian Unitary Ensemble in the large matrix limit nâ†’ âˆž. This is done byâ€¦ (More)

Using a systematic approach to evaluate Fredholm determinants numerically, we provide convincing evidence that the Airy1-process, arising as a limit law in stochastic surface growth, is not the limitâ€¦ (More)