吉林大学学报（理学版）
吉林大學學報（理學版）
길림대학학보（이학판）
JOURNAL OF JILIN UNIVERSITY(SCIENCE EDITION)
2010年
1期
26-32
,共7页
矩阵方程%正定解%迭代方法
矩陣方程%正定解%迭代方法
구진방정%정정해%질대방법
matrix equation%positive definite solution%iterative method
研究矩阵方程X-A~*A~(-α)A-B~*X~(-β)B=I在α,β∈(0,1]时的正定解, 给出了该方程有正定解的充要条件, 得到了方程有唯一正定解的必要条件及求该解的迭代方法, 并给出了求解该方程的两种迭代公式.
研究矩陣方程X-A~*A~(-α)A-B~*X~(-β)B=I在α,β∈(0,1]時的正定解, 給齣瞭該方程有正定解的充要條件, 得到瞭方程有唯一正定解的必要條件及求該解的迭代方法, 併給齣瞭求解該方程的兩種迭代公式.
연구구진방정X-A~*A~(-α)A-B~*X~(-β)B=I재α,β∈(0,1]시적정정해, 급출료해방정유정정해적충요조건, 득도료방정유유일정정해적필요조건급구해해적질대방법, 병급출료구해해방정적량충질대공식.
The positive definite solutions of the matrix equation X-A~*A~(-α)A-B~*X~(-β)B=I, α,β∈(0,1] were investigated. Necessary and sufficient conditions for the existence of positive definite solutions were derived, which generalize the existing related results. A necessary condition for the existence of the equation to have only a solution and the iterative formula for this solution were obtained. Finally, we got an inverse iterative method for solving the equation.
