We develop a new perspective on the unique maximal decomposition of an arbitrary affine permutation into a product of cyclically decreasing elements, implicit in work of Thomas Lam [Lam06]. This decomposition is closely related to the affine code, which generalizes the kbounded partition associated to Grassmannian elements. We also prove that the affine code readily encodes a number of basic co...

School of Basic Science Mathematics Section Master in Mathematical Engineering FETI-DP Domain Decomposition Method by Christoph Jäggli FETI-DP is a dual iterative, nonoverlapping domain decomposition method. By a Schur complement procedure, the solution of a boundary value problem is reduced to solving a symmetric and positive definite dual problem in which the variables are directly related to...

The purpose of this paper is to provide two numerical methods for solving the elastic body-plate problem by nonoverlapping domain decomposition type techniques, based on the discretization method by Wang. The first one is similar to an older method, but here the corresponding Schur complement matrix is preconditioned by a specific preconditioner associated with the plate problem. The second one...

Newton’s method for the inverse matrix pth root, A−1/p, has the attraction that it involves only matrix multiplication. We show that if the starting matrix is cI for c ∈ R then the iteration converges quadratically to A−1/p if the eigenvalues of A lie in a wedge-shaped convex set containing the disc { z : |z−cp| < cp }. We derive an optimal choice of c for the case where A has real, positive ei...

In this paper, the decomposition of nD-rotations is studied. Using this decomposition, nD-rotations are classified and properties are underlined. For each class, an algorithm previously presented by the authors to decompose nD-rotation into planar rotations is proposed and a generalized algorithm is presented. Moreover, an alternate algorithm based on the Schur decomposition is investigated. A ...

The rational Krylov sequence (RKS) method can be seen as a generalisation of Arnoldi’s method. It projects a matrix pencil onto a smaller subspace; this projection results in a small upper Hessenberg pencil. As for the Arnoldi method, RKS can be restarted implicitly, using the QR decomposition of a Hessenberg matrix. This restart comes with a projection of the subspace using a rational function...

A hybrid linear solver based on the Schur complement method has great potential to be a general purpose solver scalable on tens of thousands of processors. For this, it is imperative to exploit two levels of parallelism; namely, solving independent subdomains in parallel and using multiple processors per subdomain. This hierarchical parallelism can lead to a scalable implementation which mainta...

We present a spatial domain decomposition (DD) method for the solution of discretized parabolic linear–quadratic optimal control problems. Our DD preconditioners are extensions of Neumann-Neumann DD methods, which have been successfully applied to the solution of single elliptic partial differential equations and of linear–quadratic optimal control problems governed by elliptic equations. We us...

The Schur group of a commutative ring, R, with identity consists of all classes in the Brauer group of R which contain a homomorphlc image of a group ring RG for some finite group G. It is the purpose of ths article to continue an investigation of this group which was introduced in earler work as a natural gene=allzatlon of the Schur group of a field. We generalize certain facts pertaining to t...