New Alternately Linearized Implicit Iteration for M-matrix Algebraic Riccati Equations
نویسندگان
چکیده
منابع مشابه
Highly 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...
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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...
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This paper is concerned with the relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Algebraic Riccati Equations (MARE) XDX −AX −XB + C = 0 by which we mean the following conformally partitioned matrix ( B −D −C A ) is a nonsingular or an irreducible singular M -matrix. It is known that such an MARE has a unique minimal nonnegative solution Φ. ...
متن کاملDeflating Irreducible Singular M- Matrix Algebraic Riccati Equations
A deflation technique is presented for an irreducible singular M -matrix Algebraic Riccati Equation (MARE). The technique improves the rate of convergence of a doubling algorithm, especially for an MARE in the critical case for which without deflation the doubling algorithm converges linearly and with deflation it converges quadratically. The deflation also improves the conditioning of the MARE...
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Among numerous iterative methods for solving the minimal nonnegative solution of an M -matrix algebraic Riccati equation, the structure-preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1=2. In this paper...
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ژورنال
عنوان ژورنال: Journal of Mathematical Study
سال: 2017
ISSN: 1006-6837,2617-8702
DOI: 10.4208/jms.v50n1.17.04