Application of ADI Iterative Methods to the Restoration of Noisy Images
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
Solution of the matrix equation AX + XB = C [F4]
Communications of the ACM
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
An efficient algorithm for damper optimization for linear vibrating systems using Lyapunov equation
Journal of Computational and Applied Mathematics
A Fast Newton's Method for a Nonsymmetric Algebraic Riccati Equation
SIAM Journal on Matrix Analysis and Applications
Explicit Solutions for a Riccati Equation from Transport Theory
SIAM Journal on Matrix Analysis and Applications
The Smoothed Spectral Abscissa for Robust Stability Optimization
SIAM Journal on Optimization
Technical Communique: Some geometric properties of Lyapunov equation and LTI system
Automatica (Journal of IFAC)
| Hi-index | 7.29 |
This paper deals with an efficient algorithm for optimization of the solution of the parameter-dependent Sylvester equation (A"0-vC"1C"2^T)X(v)+X(v)(B"0-vD"1D"2^T)=E, where A"0, B"0 are mxm and nxn matrices, respectively. Further, C"1 and C"2 are mxr"1, D"1 and D"2 are nxr"2 and X, E are mxn matrices, while v is real parameter. For optimization we use the following two optimization criteria: Tr(X(v))-min and @?X(v)@?"F-min. We present an efficient algorithm based on derived formulas for the trace and for the Frobenius norm of the solution X as functions v-Tr(X(v)) and v-@?X(v)@?"F as well as for derivatives of these functions. That ensures fast optimization of these functions via standard optimization methods like Newton's method. A special case of this problem is a very important problem of damper viscosity optimization in mechanical systems.