Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also includes a relatively small number of off-diagonal coefficients, selected according to the excitation amplitudes undergoing the largest change in the coupled ...

i) The coupled-cluster equations being nonlinear, they have to be solved iteratively. An insight into the convergence properties of this iteration can be obtained by analysing the stability of the converged solutions as fixed points. (ii) The usual form of coupled-cluster equations represents an example to the method of moments, with the number of unknown amplitudes being equal to the number of...

The controllability and observability Gramians of time-invariant linear systems are given by the solutions of two coupled Lyapunov equations. These Gramians play an essential role in many areas of control theory such as computing Hankel singular values, system balaning, and related model reduction algorithms. We investigate the numerical solution of coupled Lyapunov equations by iterations for ...

‎The purpose of this paper is to solve two types of Lyapunov equations and quadratic matrix equations by using the spectral representation‎. ‎We focus on solving Lyapunov equations $AX+XA^*=C$ and $AX+XA^{T}=-bb^{T}$ for $A‎, ‎X in mathbb{C}^{n times n}$ and $b in mathbb{C} ^{n times s}$ with $s < n$‎, ‎which $X$ is unknown matrix‎. ‎Also‎, ‎we suggest the new method for solving quadratic matri...

the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...

We consider Magnus integrators to solve linear-quadratic N-player differential games. These problems require to solve, backward in time, non-autonomous matrix Riccati differential equations which are coupled with the linear differential equations for the dynamic state of the game, to be integrated forward in time. We analyze different Magnus integratorswhich can provide either analytical or num...

A full discrete two-level postprocessing Fourier Galerkin scheme for the unsteady Navier-Stokes equations with periodic boundary conditions is proposed in this talk. By defining a new projection, the interaction between the large and small eddies is reflected by the associated space splitting to some extent. Then a weakly coupled system of the large and small eddies is obtained. Stability and e...

the computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. it is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of new-ton&apos;s method, but previous researchers have mentioned that some...

An SPICE compatible model for multiple coupled nonuniform lossless transmission lines (TL's) is presented. The method of the modeling is based on the steplines approximation of the nonuniform TLs and quasi-TEM assumptions. Using steplines approximation the system of coupled nonuniform TLs is subdivided into arbitrary large number of coupled uniform lines (steplines) with different characteristi...

A FORTRAN 77 program is presented which calculates with the relative machine precision potential curves and matrix elements of the coupled adiabatic radial equations for a hydrogen-like atom in a homogeneous magnetic field. The potential curves are eigenvalues corresponding to the angular oblate spheroidal functions that compose adiabatic basis which depends on the radial variable as a paramete...