It is a well-known fact that the Krylov space K j ( H , x ) generated by skew-Hamiltonian matrix ? R 2 n × and some isotropic for any N . For given subspace L ? of dimension —which called Lagrangian subspace—the question whether can be as considered. The affine variety HK all matrices generate analyzed. Existence uniqueness results are proven, found with minimal 2-norm, Frobenius norm prescribe...

The Alternating Direction Multipliers Method (ADMM) is a very popular and powerful algorithm for the solution of many optimization problems. In recent years it has been widely used ill-posed inverse However, one its drawback possibly high computational cost, since at each iteration, requires large-scale least squares problem. this work we propose computationally attractive implementation ADMM, ...

The rational Krylov space is recognized as a powerful tool within Model Order Reduction techniques for linear dynamical systems. However, its success has been hindered by the lack of a parameter-free procedure, which would effectively generate the sequence of shifts used to build the space. In this paper we propose an adaptive computation of these shifts. The whole procedure only requires to in...

with a symmetric and positive definite operator A defined on a Hilbert space V with dimV = N and its preconditioned version PCG. We derive the CG from the projection in A-inner product point of view. We shall use (·, ·) for the standard inner product and (·, ·)A for the inner product introduced by the SPD operator A. When we say ‘orthogonal’ vectors, we refer to the default (·, ·) inner product...

In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability and others. We show how to apply Krylov-type methods such as the extended block Arnoldi algorithm to get low rank approximate solutions. The initial proble...

In a number of applications in scientific computing and engineering one has to solve huge sparse linear systems of equations with several right-hand sides that are given at once. Block Krylov space solvers are iterative methods that are especially designed for such problems and have fundamental advantages over the corresponding methods for systems with a single right-hand side: much larger sear...

Kaltofen has proposed a new approach in [8] for computing matrix determinants. The algorithm is based on a baby steps/giant steps construction of Krylov subspaces, and computes the determinant as the constant term of a characteristic polynomial. For matrices over an abstract field and by the results of Baur and Strassen [1], the determinant algorithm, actually a straight-line program, leads to ...

The most popular iterative linear solvers in Computational Fluid Dynamics (CFD) calculations are restarted GMRES and BiCGStab. At the beginning of most incompressible flow calculations, the computation time and the number of iterations to converge for the pressure Poisson equation are quite high, since the initial guess is far from the solution. In this case, the BiCGStab algorithm, with relati...

In this paper, we propose two models reduction algorithms for approximation of large-scale linear switched systems. We present at first the iterative dual rational krylov approach, that construct a union of krylov subspaces. The iterative dual rational Krylov is low in cost, numerical efficient but the stability of reduced system is not always guaranteed. In the second part we present, the iter...