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Lyapunov equation
"... The following conjecture relates the eigenvalues of certain matrices that are derived from the solution of a Lyapunov equation that occurred in the analysis of stochastic subspace identification algorithms [3]. First, we formulate the conjecture as a pure matrix algebraic problem. In Section 2, we w ..."
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The following conjecture relates the eigenvalues of certain matrices that are derived from the solution of a Lyapunov equation that occurred in the analysis of stochastic subspace identification algorithms [3]. First, we formulate the conjecture as a pure matrix algebraic problem. In Section 2, we
Numerical Solution of Generalized Lyapunov Equations
 Adv. Comp. Math
, 1996
"... Two efficient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The first one is a generalization of the BartelsStewart method and the second is an extension of Hammarling's method to generalized Lyapunov equations. Our LAPACK based subr ..."
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Cited by 48 (0 self)
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Two efficient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The first one is a generalization of the BartelsStewart method and the second is an extension of Hammarling's method to generalized Lyapunov equations. Our LAPACK based
Low rank solutions of Lyapunov equations
 SIAM Journal Matrix Anal. Appl
, 2002
"... Abstract. This paper presents the Cholesky factor–alternating direction implicit (CF–ADI) algorithm, which generates a low rank approximation to the solution X of the Lyapunov equation AX +XAT = −BBT. The coefficient matrix A is assumed to be large, and the rank of the righthand side −BBT is assume ..."
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Cited by 106 (4 self)
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Abstract. This paper presents the Cholesky factor–alternating direction implicit (CF–ADI) algorithm, which generates a low rank approximation to the solution X of the Lyapunov equation AX +XAT = −BBT. The coefficient matrix A is assumed to be large, and the rank of the righthand side −BBT
PARALLEL SOLUTION OF LARGE LYAPUNOV EQUATIONS*
"... Abstract. In this paper two algorithms for the solution of largeorder (100 _< n _< 1000) Lyapunov equations AX + XA T + Q 0 are presented. First, a parallel version of the Hammarling algorithm for the solution of Lyapunov equations where the coefficient matrix A is large and dense is presente ..."
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Abstract. In this paper two algorithms for the solution of largeorder (100 _< n _< 1000) Lyapunov equations AX + XA T + Q 0 are presented. First, a parallel version of the Hammarling algorithm for the solution of Lyapunov equations where the coefficient matrix A is large and dense
Numerical solution of the stable, nonnegative definite Lyapunov equation
 IMA J. Numer. Anal
, 1982
"... We discuss the numerical solution of the Lyapunov equation ..."
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Cited by 110 (2 self)
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We discuss the numerical solution of the Lyapunov equation
Lyapunov Equations and Riccati
"... ABSTRACT: In this paper, two new types of Lyapunov and Riccati equations are presented for linear timeinvariant descriptor systems. The two equations play key roles in asymptotic stability analysis and control synthesis for this class of systems. Fundamental properties of the two equations are inv ..."
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ABSTRACT: In this paper, two new types of Lyapunov and Riccati equations are presented for linear timeinvariant descriptor systems. The two equations play key roles in asymptotic stability analysis and control synthesis for this class of systems. Fundamental properties of the two equations
using Lyapunov equation
"... efficient algorithm for damper optimization for linear vibrating systems ..."
On Bounds for the Solution of the Riccati and Lyapunov Equations *
"... Abstract: In recent years, several bounds have been reported for different measures of the “extent ” or “size” of the solution of the algebraic matrix equation arising in control theory, such as the Riccati equation and the Lyapunov equation. This paper collects the bounds that have been presented u ..."
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Abstract: In recent years, several bounds have been reported for different measures of the “extent ” or “size” of the solution of the algebraic matrix equation arising in control theory, such as the Riccati equation and the Lyapunov equation. This paper collects the bounds that have been presented
Large Periodic Lyapunov Equations: Algorithms and Applications
, 2003
"... Two algorithms for the solution of discretetime periodic Lyapunov equations are presented. ..."
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Cited by 6 (0 self)
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Two algorithms for the solution of discretetime periodic Lyapunov equations are presented.
ON THE SENSITIVITY OF THE SOLUTION OF THE GENERALIZED LYAPUNOV EQUATION
"... Abstract. Some results on the sensitivity of the solution of the generalized Lyapunov equation An−1X +An−2XA ∗ + · · ·+X(A∗)n−1 = B, are shown follow easily from wellknown theorems in functional analysis. 1. ..."
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Abstract. Some results on the sensitivity of the solution of the generalized Lyapunov equation An−1X +An−2XA ∗ + · · ·+X(A∗)n−1 = B, are shown follow easily from wellknown theorems in functional analysis. 1.
Results 1  10
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