Perturbation Theory for Algebraic Riccati Equations
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Perturbation Analysis of the Periodic Discrete-Time Algebraic Riccati Equation
SIAM Journal on Matrix Analysis and Applications
Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches
SIAM Journal on Matrix Analysis and Applications
Backward Perturbation Analysis of the Periodic Discrete-Time Algebraic Riccati Equation
SIAM Journal on Matrix Analysis and Applications
Brief paper: Perturbation analysis and condition numbers of symmetric algebraic Riccati equations
Automatica (Journal of IFAC)
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This paper is devoted to the perturbation analysis for the quadratic matrix equation X^2-EX-F=0, where E is a diagonal matrix and F is an M-matrix. The quadratic matrix equation of this type arises in noisy Wiener-Hopf problems for Markov chains. The solution of practical interest is a particular M-matrix solution. In this paper the perturbation bound of the M-matrix solution is presented, meanwhile the residual bound for an approximate solution to the M-matrix solution is obtained. The theoretical results are illustrated by using simple numerical examples.