Title :
On the extreme solutions of an nonlinear matrix equation
Author :
Guo, Xiaoxia ; Ji, Zhijian
Author_Institution :
Ocean Univ. of China, Qingdao
Abstract :
A quadratically convergent algorithm (QCA) for solving the extreme solutions of the matrix equation AX2+BX+C=0 was proposed by Bini and Meini. In this paper, we present a new derivation for this algorithm and a new proof for the convergence theory by using a structure-preserving transformation of a matrix pencil. Since only the knowledge of the elementary matrix theory is used, the derivation and the proof are very concise and pellucid.
Keywords :
matrix algebra; nonlinear equations; convergence theory; elementary matrix theory; matrix pencil; nonlinear matrix equation; quadratically convergent algorithm; structure-preserving transformation; Cities and towns; Control theory; Convergence; Design for quality; Eigenvalues and eigenfunctions; Newton method; Nonlinear equations; Quantum cellular automata; Riccati equations; Solvents;
Conference_Titel :
American Control Conference, 2007. ACC '07
Conference_Location :
New York, NY
Print_ISBN :
1-4244-0988-8
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2007.4282233
