Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing coset states in the standard approach to the hidden subgroup problem. We observe that simply measuring the partition (a procedure we call weak Schur sampling...

We present numerical methods for solving systems of linear equations originated from the discretisation of two-dimensional elliptic partial diierential equations. We are interested in diierential equations that describe heterogeneous and anisotropic phenomena. We use a nonoverlapping domain decomposition method for solving the linear systems. We describe new local preconditioners for the interf...

The large increase of unknowns in multi-domain mechanical modeling leads to investigate new parallel implementation of ODE and DAE systems. Unlike space domain decomposition, no geometrical information is given to decompose the system. The connection between unknowns have to be built to decompose the system in subsystems. A Schur Complement DDM can then be applied. During some time steps, the J...

The parallel implementation of GCR is addressed, with particular focus on communication costs associated with orthogonalization processes. This consideration brings up questions concerning the use of Householder reflections with GCR. To precondition the GCR method a block Gauss-Jacobi method is used. Approximate solvers are used to obtain a solution of the diagonal blocks. Experiments on a clus...

This paper mainly treats of the interconnections between the periodic Schur form and its associated periodical deflating subspaces. We establish some equivalent statements of the periodic Schur decomposition for regular periodic matrix pairs. Based on these equivalences, we define the eigenspaces for regular periodic matrix pairs, and point out the corresponding eigenvalues inherited from a giv...

in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...

In this paper, we propose a nonoverlapping domain decomposition method for solving the three-dimensional Maxwell equations, based on the edge element discretization. For the Schur complement system on the interface, we construct an efficient preconditioner by introducing two special coarse subspaces defined on the nonoverlapping subdomains. It is shown that the condition number of the precondit...

We propose a new domain decomposition method for the Stokes equations in two and three dimensions. The algorithm, we propose, is very similar to an algorithm which is obtained by a Richardson iteration of the Schur complement equation using a Neumann-Neumann preconditioner. A comparison of both methods with the help of a Fourier analysis shows clearly the advantage of the new approach. This cou...

Given a complex matrix H, we consider the decomposition H = QRP∗, where R is upper triangular and Q and P have orthonormal columns. Special instances of this decomposition include the singular value decomposition (SVD) and the Schur decomposition where R is an upper triangular matrix with the eigenvalues of H on the diagonal. We show that any diagonal for R can be achieved that satisfies Weyl’s...

The canonical decomposition of higher-order tensors is a key tool in multilinear algebra. First we review the state of the art. Then we show that, under certain conditions, the problem can be rephrased as the simultaneous diagonalization, by equivalence or congruence, of a set of matrices. Necessary and sufficient conditions for the uniqueness of these simultaneous matrix decompositions are der...