For iterative sequences that converge to the solution set of a linear matrix inequality, we show that the distance of the iterates to the solution set is at most O(2 ?d). The nonnegative integer d is the so{called degree of singularity of the linear matrix inequality, and denotes the amount of constraint violation in the iterate. For infeasible linear matrix inequalities, we show that the minim...

A real n × n symmetric matrix X = (x i j)n×n is called a bisymmetric matrix if x i j = xn+1− j,n+1−i . Based on the projection theorem, the canonical correlation decomposition and the generalized singular value decomposition, a method useful for finding the least-squares solutions of the matrix equation AXA= B over bisymmetric matrices is proposed. The expression of the least-squares solutions ...

In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...

We present a high-order hybridizable discontinuous Galerkin method for solving elliptic interface problems in which the solution and gradient are nonsmooth because of jump conditions across the interface. The hybridizable discontinuous Galerkin method is endowed with several distinct characteristics. First, they reduce the globally coupled unknowns to the approximate trace of the solution on el...

We consider the bandwidth provisioning problem in service overlay networks (SON). We formulate the bandwidth provisioning problem in an optimization framework taking the stochastic processes involved into consideration. First, we provide the optimal solution that maximizes the expected net revenue in a single-link network under stationary traffic demand. Then, we show that the revenue maximizat...

In this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. This system is solved iteratively, where the applicationof the infinite stiffness matrix, that is sufficiently compressible,is r...