The multigrid waveform relaxation (WR) algorithm has been fairly studied and implemented for parabolic equations. It has been found that the performance of the multigrid WR method for a parabolic equation is practically the same as that of multigrid iteration for the associated steady state elliptic equation. However, the properties of the multigrid WR method for hyperbolic problems are relativ...

Context. New high-resolution spectropolarimetric observations of solar prominences require improved radiative modelling capabilities in order to take into account both multi-dimensional – at least 2D – geometry and complex atomic models. Aims. This makes necessary the use of very fast numerical schemes for the resolution of 2D non–LTE radiative transfer problems considering freestanding and ill...

Step-asynchronous successive overrelaxation updates the values contained in a single vector using the usual Gauß–Seidel-like weighted rule, but arbitrarily mixing old and new values, the only constraint being temporal coherence— you cannot use a value before it has been computed. We show that given a nonnegative real matrix A, a σ ≥ ρ(A) and a vector w > 0 such that Aw ≤ σw, every iteration of ...

We present a very robust and efficient scheme for 3-D reconstruction from point correspondences over multiple images taken by uncalibrated cameras. Our method is based on iterative projective reconstruction followed by Euclidean upgrading. We accelerate the time-consuming iterations for projective reconstruction by using the power method for eigenvalue computation, accelerating the power method...

We present some computational experimentation for solving a linear system Ax = b by applying the Triangle Algorithm described in [3], based on converting the system to a convex hull problem as described in [4]. A comparison of the performance with classical iterative methods such as Jacobi, Gauss-Seidel, and Successive Over-Relaxation method for small size problems suggests the Triangle Algorit...

Michael Neumann t Department of Mathematics University of Connecticut . Storrs, CT 06269-3009. Because the spectral radius is only an asymptotic measure of the rate of convergence of a linear iterative method, Golub and dePillis have raised in a recent paper the question of determining, for each k ~ 1, a relaxation parameter w E (0,2) and a pair of relaxation parameters WI and W2 which minimize...

We extend Krylov subspace methods, which are intended for iterative solution of systems of linear equations, to a function space for the solution of cicuit problems. Four of the previously untried methods are applied to a tightly coupled circuit to illustrate the convergence properties of these methods. Numerical results showed that convergence was achieved for many cases where the conventional...

A lateral boundary treatment using summation-by-parts operators and simultaneous approximation terms is introduced. The method is similar to Davies relaxation technique used in the weather prediction community and have similar areas of application, but is also provably stable. In this paper, it is shown how this technique can be applied to the shallow water equations, and that it reduces the er...

The LP relaxation for the Priority Steiner Tree is similar to the relaxation used before for the Steiner Tree. Again, say a set S ⊆ V crosses the set R if S ∩ R 6= ∅ and R \S 6= ∅ there is at least one terminal in S and one not in S. For j ≤ k, let Sj be the collection of all sets which cross Rj . Finally, for a set S ⊆ V , let ∂S be the set of edges with one endpoint in S and one in V \S. Defi...

Most discussion among players of the modern classical guitar regarding the early 19century guitar has been backward looking, that is, either looking at ways of playing this repertoire on a modern instrument in a modern style, or how to imitate the stylistic features of the period on a modern guitar. I will focus instead on coming towards Sor and his contemporaries from before their period, as c...