Two kinds of condition numbers for the quadratic matrix equation

作者: Lan-dong Liu , Xin Lu

DOI: 10.1016/J.AMC.2013.02.048

关键词:

摘要: In the situation that quadratic matrix equation has dominant or minimal solvents, mixed and componentwise condition numbers of are considered. The explicit approximate expressions two kinds derived in uniform manner, upper bounds proposed. theoretical results illustrated by using some simple numerical examples.

参考文章(39)
Jun-Feng Yin, Zhong-Zhi Bai, Xiao-Xia Guo, ON TWO ITERATION METHODS FOR THE QUADRATIC MATRIX EQUATION INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING. ,vol. 2, pp. 114- 122 ,(2005)
Dai, Bai, Zhong-Zhi, Hua, ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS 计算数学:英文版. ,vol. 29, pp. 341- 366 ,(2011)
Gao, Bai, Yong-Hua, Zhong-Zhi, MODIFIED BERNOULLI ITERATION METHODS FOR QUADRATIC MATRIX EQUATION 计算数学:英文版. ,vol. 25, pp. 498- 511 ,(2007)
AnpingLiao, ZhongzhiBai, LEAST—SQUARES SOLUTION OF AXB=D OVER SYMMETRIC POSITIVE SEMIDEFINITE MATRICES X 计算数学:英文版. ,vol. 21, pp. 175- 182 ,(2003)
Jian-Chen Zhang, Shu-Zi Zhou, Xi-Yan Hu, The (P,Q) generalized reflexive and anti-reflexive solutions of the matrix equation AX=B Applied Mathematics and Computation. ,vol. 209, pp. 254- 258 ,(2009) , 10.1016/J.AMC.2008.12.059
Felipe Cucker, Huaian Diao, Yimin Wei, On mixed and componentwise condition numbers for Moore–Penrose inverse and linear least squares problems Mathematics of Computation. ,vol. 76, pp. 947- 963 ,(2006) , 10.1090/S0025-5718-06-01913-2
John E Dennis, Jr, Joseph F Traub, Robert P Weber, None, The Algebraic Theory of Matrix Polynomials SIAM Journal on Numerical Analysis. ,vol. 13, pp. 831- 845 ,(1976) , 10.1137/0713065
Yong-Hua Gao, Newton’s method for the quadratic matrix equation Applied Mathematics and Computation. ,vol. 182, pp. 1772- 1779 ,(2006) , 10.1016/J.AMC.2006.06.014
Françoise Tisseur, Karl Meerbergen, The Quadratic Eigenvalue Problem SIAM Review. ,vol. 43, pp. 235- 286 ,(2001) , 10.1137/S0036144500381988