منابع مشابه
Lyapunov equation
This chapter is about numerical methods for a particular type of equation expressed as a matrix equality. The Lyapunov equation is the most common problem in the class of problems called matrix equations. Other examples of matrix equations: Sylvester equation, Stein equation, Riccati equation. Definition 5.0.1 Consider two square matrices A, W ∈ Rn×n. The problem to find a square matrix X ∈ Rn×...
متن کاملFactorized solution of the Lyapunov equation by using the hierarchical matrix arithmetic ∗
We investigate the solution of the Lyapunov equation with the matrix sign function method. In order to obtain the factorized solution we use a partitioned Newton iteration, where one part of the iteration uses formatted arithmetic for the hierarchical matrix format while the other part converges to an approximate full-rank factor of the solution.
متن کاملEla New Estimates for the Solution of the Lyapunov Matrix Differential Equation∗
In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.
متن کاملNew estimates for the solution of the Lyapunov matrix differential equation
In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.
متن کاملBounds on the trace of a solution to the Lyapunov equation with a general stable matrix
Some new estimates for the eigenvalue decay rate of the Lyapunov equation AX + XA = B with a low rank right-hand side B are derived. The new bounds show that the right-hand side B can greatly influence the eigenvalue decay rate of the solution. This suggests a new choice of the ADI-parameters for the iterative solution. The advantage of these new parameters is illustrated on second order damped...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1979
ISSN: 0024-3795
DOI: 10.1016/0024-3795(79)90117-4