TY - JOUR

T1 - Convex invertible cones of matrices - A unified framework for the equations of Sylvester, Lyapunov and Riccati

AU - Lewkowicz, Izchak

PY - 1999/1/1

Y1 - 1999/1/1

N2 - Convex cones of matrices which are closed under matrix inversion were defined and various connections with the algebraic Lyapunov equation of general inertia were studied in (N. Cohen, I. Lewkowicz, Linear Algebra and its Appl. 250 (1997) 105-131). Here, in the price of doubling the size of the matrices involved, we introduce a unified framework for the equations of Sylvester, Lyapunov and Riccati. This enables one to extend the convex invertible cone structure to all these three equations and explore related properties. In particular, the use of the Matrix Sign Function for solving these equations is examined.

AB - Convex cones of matrices which are closed under matrix inversion were defined and various connections with the algebraic Lyapunov equation of general inertia were studied in (N. Cohen, I. Lewkowicz, Linear Algebra and its Appl. 250 (1997) 105-131). Here, in the price of doubling the size of the matrices involved, we introduce a unified framework for the equations of Sylvester, Lyapunov and Riccati. This enables one to extend the convex invertible cone structure to all these three equations and explore related properties. In particular, the use of the Matrix Sign Function for solving these equations is examined.

UR - http://www.scopus.com/inward/record.url?scp=0007291438&partnerID=8YFLogxK

U2 - 10.1016/S0024-3795(98)10164-7

DO - 10.1016/S0024-3795(98)10164-7

M3 - Article

AN - SCOPUS:0007291438

VL - 286

SP - 107

EP - 133

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -