Numerical solution of generalized Lyapunov equations

Low-rank Iterative Methods for Projected Generalized Lyapunov Equations

LOW-RANK ITERATIVE METHODS FOR PROJECTED GENERALIZED LYAPUNOV EQUATIONS TATJANA STYKEL Abstract. We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximat...

On the numerical solution of generalized Sylvester matrix equations

‎The global FOM and GMRES algorithms are among the effective‎ ‎methods to solve Sylvester matrix equations‎. ‎In this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two CG-type algorithms for solving generalized Sylvester matrix‎ ‎equations‎. ‎The proposed methods are iterative projection metho...

The Taylor Method for Numerical Solution of Fuzzy Generalized Pantograph Equations with Linear Functional Argument

Efficient low-rank solution of generalized Lyapunov equations

An iterative method for the low-rank approximate solution of a class of generalized Lyapunov equations is studied. At each iteration, a standard Lyapunov is solved using Galerkin projection with an extended Krylov subspace method. This Lyapunov equation is solved inexactly, thus producing a nonstationary iteration. Several theoretical and computational issues are discussed so as to make the ite...

Approximated solution of First order Fuzzy Differential Equations under generalized differentiability

In this research, a numerical method by piecewise approximated method for solving fuzzy differential equations is introduced. In this method, the solution by piecewise fuzzy polynomial is present. The base of this method is using fuzzy Taylor expansion on initial value of fuzzy differential equations. The existence, uniqueness and convergence of the approximate solution are investigated. To sho...