Existence, localization and approximation of solution of symmetric algebraic Riccati equations

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Abstract

In this paper we consider a family of high-order iterative methods which is more efficient than the Newton method to approximate a solution of symmetric algebraic Riccati equations. In fact, this paper is devoted to the convergence study of a k-steps iterative scheme with low operational cost and high order of convergence. We analyze their accessibility and computational efficiency. We also obtain results about the existence and localization of solution. Numerical experiments confirm the advantageous performance of the iterative scheme analyzed.

Keywords

Algebraic Riccati equations
High order iterative schemes
Lyapunov equations
Local convergence

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The research has been partially supported by the project MTM2014-52016-C2-1-P of the Spanish Ministry of Economy and Competitiveness.