지원사업
학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
커뮤니티
연구자들이 자신의 연구와 전문성을 널리 알리고, 새로운 협력의 기회를 만들 수 있는 네트워킹 공간이에요.
초록· 키워드
오류제보하기
This paper is concerned with the positive definite solutions of the nonlinear matrix equation $X-A^{*}\bar{X}^{-1}A=Q$, where $A, Q$ are given complex matrices with $Q$ positive definite. We show that such a matrix equation always has a unique positive definite solution and if $A$ is nonsingular, it also has a unique negative definite solution. Moreover, based on Sherman-Morrison-Woodbury formula, we derive elegant relationships between solutions of $X-A^{*}\bar{X}^{-1}A=I$ and the well-studied standard nonlinear matrix equation $Y+B^{*}Y^{-1}B=Q$, where $B, Q$ are uniquely determined by $A$. Then several effective numerical algorithms for the unique positive definite solution of $X-A^{*}\bar{X}^{-1}A=Q$ with linear or quadratic convergence rate such as inverse-free fixed-point iteration, structure-preserving doubling algorithm, Newton algorithm are proposed. Numerical examples are presented to illustrate the effectiveness of all the theoretical results and the behavior of the considered algorithms.
목차
등록된 정보가 없습니다.
참고문헌 (28)
참고문헌 신청
M. Berzig / 2012 / Positive definite solution of the matrix equation $X\;=\;Q\;-\;A*X^{-1}\;A+B*X^{-1}\;B$ via Bhaskar-Lakshmikantham fixed point theorem / Math. Sci. (Springer) 6:55~62
J. H. Bevis / 1986 / Consimilarity and the matrix equation $A{\overline{X}}\;-\;XB\;=\;C$ , in Current trends in matrix theory :51~64
J. H. Bevis / 1988 / The matrix equation $A{\overline{X}}\;-\;XB\;=\;C$ and its special cases / SIAM J. Matrix Anal. Appl. 9(3):348~359
R. Bhatia / 1997 / Matrix Analysis, Graduate Texts in Mathematics, 169 / Springer-Verlag
M. T. Chu / 2016 / On the first degree Fej er-Riesz factorization and its applications to $X\;+\;A*X^{-1}\;A\;=\;Q$ / Linear Algebra Appl. 489:123~143
J. H. Bevis / 1986 / Consimilarity and the matrix equation
J. H. Bevis / 1988 / The matrix equation
R. Bhatia / 1997 / Matrix Analysis, Graduate Texts in Mathematics, 169 / Springer-Verlag
M. T. Chu / 2016 / On the first degree Fej er-Riesz factorization and its applications to
함께 읽어보면 좋을 논문
논문 유사도에 따라 DBpia 가 추천하는 논문입니다. 함께 보면 좋을 연관 논문을 확인해보세요!
-
Newton Schulz method for solving nonlinear matrix equation $X^p + {A^*}XA=Q$
대한수학회지
2018 .01
-
HERMITIAN POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X8+A*X-tA = Q
대한수학회지
2017 .01
-
Local convergence of functional iterations for solving a quadratic matrix equation
대한수학회보
2017 .01
-
On Newton's Method for Solving a System of Nonlinear Matrix Equations
East Asian Mathematical Journal
2019 .01
-
ACCELERATION OF MACHINE LEARNING ALGORITHMS BY TCHEBYCHEV ITERATION TECHNIQUE
JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
2018 .03
-
An adaptive primal-dual full-Newton step infeasible interior-point algorithm for linear optimization
대한수학회보
2016 .01
-
A NEW APPROACH FOR NUMERICAL SOLUTION OF LINEAR AND NON-LINEAR SYSTEMS
Journal of applied mathematics & informatics
2017 .01
-
A homotopy continuation method for solving a matrix equation
대한수학회지
2018 .01
-
Applications of the coupled fixed point theorem to the nonlinear matrix equations
대한수학회지
2018 .01
-
Thomas algorithms for systems of fourth-order finite difference methods
대한수학회지
2022 .09
-
On the Pocklington-Peralta square root algorithm in finite fields
대한수학회보
2022 .11
-
Convergence of Nowton's Method for Solving a Nonlinear Matrix Equation
East Asian Mathematical Journal
2016 .01
-
AN ITERATIVE ALGORITHM FOR THE LEAST SQUARES SOLUTIONS OF MATRIX EQUATIONS OVER SYMMETRIC ARROWHEAD MATRICES
대한수학회지
2015 .01
-
FINITE-DIFFERENCE BISECTION ALGORITHMS FOR FREE BOUNDARIES OF AMERICAN OPTIONS
JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
2015 .03
-
Numerical methods for Fuzzy system of linear equations with crisp coefficient
순수 및 응용수학
2020 .01
-
Approximate projection algorithms for solving equilibrium and multivalued variational inequality problems in Hilbert space
대한수학회보
2022 .07
-
A new algorithm for variational inclusion problem
한국수학논문집
2021 .12
-
AN ACCELERATING SCHEME OF CONVERGENCE TO SOLVE FUZZY NON-LINEAR EQUATIONS
순수 및 응용수학
2017 .01
-
Geodesic Clustering for Covariance Matrices
CSAM(Communications for Statistical Applications and Methods)
2015 .07
-
The computation of positive solutions for a boundary value problem of the linear beam equation
대한수학회논문집
2017 .01
이 논문의 저자 정보
최근 본 자료
댓글(0)
0