Fast sweeping methods are efficient Gauss–Seidel iterative numerical schemes originally designed for solving static Hamilton–Jacobi equations. Recently, these methods have been applied to solve hyperbolic conservation laws with source terms. In this paper, we propose Lax–Friedrichs fast sweeping multigrid methods which allow even more efficient calculations of viscosity solutions of stationary ...

The proof will show that the resolvent of (the Friedrichs extension of a restriction of) the invariant Laplacian is compact. Let Lη be the subspace of L 2 = L(PGLr(Z)\PGLr(R)/O(n,R)) with all constant terms vanishing above given fixed heights (specified by a real-valued function η on simple positive roots, described precisely below). By its construction, the resolvent of the Friedrichs extensio...

Speakers are able to speak in synchrony to another speaker or to a recording of another speaker. The present research studied whether and, if yes, speakers change their speech rhythm when synchronizing to another speaker. We developed a measure (SRratio) which monitors on a scale between 0 and 1 whether the durational characteristics of a speaker’s synchronous speech are closer to his/her own r...

In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are consistent with the one-sided Lipschitz condition (OSLC): Lax-Friedrichs, Engquist-Osher and Godunov. We mainly focus on the inviscid Burgers equation, for which we know that the...

We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to regular even order quasi-differential expression Shin-Zettl type. The characterization is stated in terms specially chosen basis for kernel maximal and employs description Friedrichs due Möller Zettl.