In this talk, we present an efficient method for a convex optimization problem involving a large non-symmetric and non-Toeplitz matrix. The proposed method is an instantiation of ADMM (Alternating Direction Method of Multipliers) applied in Krylov subspaces. Our method shows a significant advantage in computational time for convex optimization problems involving general matrices of large size. ...

The paper studies multigrid methods for solving systems of linear algebraic equations resulting from the seven-point discretization three-dimensional Dirichlet problem an elliptic differential equation second order in a parallepipedal domain on regular grid. algorithms suggested are presented as special iteration processes incomplete factorization Krylov subspaces with hierarchical recursive ve...

‎the global generalized minimum residual (gl-gmres)‎ ‎method is examined for solving the generalized sylvester matrix equation‎ ‎[sumlimits_{i = 1}^q {a_i } xb_i = c.]‎ ‎some new theoretical results are elaborated for‎ ‎the proposed method by employing the schur complement‎. ‎these results can be exploited to establish new convergence properties‎ ‎of the gl-gmres method for solving genera...

The aim of this paper is two-fold. First, we propose an efficient implementation of the continuous time waveform relaxation method based on block Krylov subspaces. Second, we compare this new implementation against Krylov subspace methods combined with the shift and invert technique.

We will present a projection approach for model reduction of linear time-varying descriptor systems based on earlier ideas in the work of Philips and others. The idea behind the proposed procedure is based on a multipoint rational approximation of the monodromy matrix of the corresponding differential-algebraic equation. This is realized by orthogonal projection onto a rational Krylov subspace....

We will present a projection approach for model reduction of linear time-varying descriptor systems based on earlier ideas in the work of Philips and others. The idea behind the proposed procedure is based on a multipoint rational approximation of the monodromy matrix of the corresponding differential-algebraic equation. This is realized by orthogonal projection onto a rational Krylov subspace....

Many problems in scientific computing involving a large sparse matrix A are solved by Krylov subspace methods. This includes methods for the solution of large linear systems of equations with A, for the computation of a few eigenvalues and associated eigenvectors of A, and for the approximation of nonlinear matrix functions of A. When the matrix A is non-Hermitian, the Arnoldi process commonly ...