Mixed and componentwise condition numbers of nonsymmetric algebraic Riccati equation

Abstract In this paper, the mixed and componentwise condition numbers of nonsymmetric algebraic Riccati equation are considered. The explicit expressions of two kinds of condition numbers are derived in the uniform manner, and the upper bounds are proposed. Some simple numerical experiments show that the mixed and componentwise condition numbers can be sharp.

[1]  Israel Koltracht,et al.  Mixed componentwise and structured condition numbers , 1993 .

[2]  Wen-Wei Lin,et al.  Nonsymmetric Algebraic Riccati Equations and Hamiltonian-like Matrices , 1998, SIAM J. Matrix Anal. Appl..

[3]  Chun-Hua Guo,et al.  A new class of nonsymmetric algebraic Riccati equations , 2007 .

[4]  Hua Xiang,et al.  Structured mixed and componentwise condition numbers of some structured matrices , 2007 .

[5]  Ji-guang Sun SENSITIVITY ANALYSIS OF THE DISCRETE-TIME ALGEBRAIC RICCATI EQUATION , 1998 .

[6]  Wen-Wei Lin,et al.  A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation , 2006, Numerische Mathematik.

[7]  Chun-Hua Guo,et al.  Nonsymmetric Algebraic Riccati Equations and Wiener-Hopf Factorization for M-Matrices , 2001, SIAM J. Matrix Anal. Appl..

[8]  Yimin Wei,et al.  Perturbation analysis and condition numbers of symmetric algebraic Riccati equations , 2009, Autom..

[9]  Alan J. Laub,et al.  On the Iterative Solution of a Class of Nonsymmetric Algebraic Riccati Equations , 2000, SIAM J. Matrix Anal. Appl..

[10]  Bruno Iannazzo,et al.  A Fast Newton's Method for a Nonsymmetric Algebraic Riccati Equation , 2008, SIAM J. Matrix Anal. Appl..

[11]  Mei Han An,et al.  accuracy and stability of numerical algorithms , 1991 .

[12]  Yimin Wei,et al.  On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems , 2006, Math. Comput..

[13]  Zhong-zhiBai,et al.  ON THE MINIMAL NONNEGATIVE SOLUTION OFNONSYMMETRIC ALGEBRAIC RICCATI EQUATION , 2005 .

[14]  Shufang Xu,et al.  Accurate solutions of M-matrix Sylvester equations , 2012, Numerische Mathematik.

[15]  N. Higham A Survey of Componentwise Perturbation Theory in Numerical Linear Algebra , 1994 .

[16]  Shufang Xu,et al.  Accurate solutions of M-matrix algebraic Riccati equations , 2012, Numerische Mathematik.

[17]  Ji-guang Sun,et al.  Condition numbers of algebraic Riccati equations in the Frobenius norm , 2002 .

[18]  Wen-Wei Lin,et al.  Perturbation Analysis of the Periodic Discrete-Time Algebraic Riccati Equation , 2002, SIAM J. Matrix Anal. Appl..

[19]  Gerhard Freiling,et al.  A survey of nonsymmetric Riccati equations , 2002 .