On inexact Newton methods based on doubling iteration scheme for symmetric algebraic Riccati equations
نویسندگان
چکیده
منابع مشابه
Inexact Kleinman-Newton Method for Riccati Equations
In this paper we consider the numerical solution of the algebraic Riccati equation using Newton's method. We propose an inexact variant which allows one control the number of the inner iterates used in an iterative solver for each Newton step. Conditions are given under which the monotonicity and global convergence result of Kleinman also hold for the inexact Newton iterates. Numerical results ...
متن کاملOn a Newton-Like Method for Solving Algebraic Riccati Equations
An exact line search method has been introduced by Benner and Byers [IEEE Trans. Autom. Control, 43 (1998), pp. 101–107] for solving continuous algebraic Riccati equations. The method is a modification of Newton’s method. A convergence theory is established in that paper for the Newton-like method under the strong hypothesis of controllability, while the original Newton’s method needs only the ...
متن کاملInexact Newton Methods for Solving Nonsmooth Equations
This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We de ne two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BD-regularity at the solution. We introduce a globally convergent inexact iteration function based method. We discuss implementati...
متن کاملHighly accurate doubling algorithms for M-matrix algebraic Riccati equations
The doubling algorithms are very efficient iterative methods for computing the unique minimal nonnegative solution to anM -matrix algebraic Riccati equation (MARE). They are globally and quadratically convergent, except for MARE in the critical case where convergence is linear with the linear rate 1/2. However, the initialization phase and the doubling iteration kernel of any doubling algorithm...
متن کاملAlternating-directional Doubling Algorithm for M-Matrix Algebraic Riccati Equations
A new doubling algorithm—the alternating-directional doubling algorithm (ADDA)— is developed for computing the unique minimal nonnegative solution of an M -matrix algebraic Riccati equation (MARE). It is argued by both theoretical analysis and numerical experiments that ADDA is always faster than two existing doubling algorithms: SDA of Guo, Lin, and Xu (Numer. Math., 103 (2006), pp. 393–412) a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2014
ISSN: 0377-0427
DOI: 10.1016/j.cam.2013.09.074