컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0593 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Analysis (real / complex / harmonic analysis) (SS-08) |
| 영문제목 (Title(Eng.)) |
On nonlinear matrix equations |
| 저자(Author(s)) |
Hyun-Min Kim1, Jong Hyeon Seo2 Department of Mathematics1, Department of Mathematics2 |
| 초록본문(Abstract) | We consider nonlinear matrix equations which are quadratic matrix equation $$ Q(X) = AX^2 +BX +C =0, $$ where $X$ is an $n\times n$ unknown complex matrix and $A$, $B$ and $C$ are $n \times n$ given matrices with complex elements and matrix polynomial $$ P(X) = A_0X^m+A_1X^{m-1}+\cdots+A_m=0, $$ $A_m, A_{m-1}, \cdots A_0$ and $X$ are real $n \times n$ matrices. The convergence of Newton method and Newton's method with exact line searches for solving $Q(X)$ and $P(X)$ is also considered. We show that an elementwise minimal nonnegative solvent can be found by these methods with the zero starting matrix. Finally functional iterations and conjugate gradient methods are applied to equations $Q(X)$ and $P(X)$, and we show some numerical experiments. |
| 분류기호 (MSC number(s)) |
15A24, 65F30, 65H10 |
| 키워드(Keyword(s)) | quadratic matrix equation, matrix polynomial, Fr\'{e}chet derivative, quadratic eigenvalue problems, M-matrix, Newton's method, exact line searches, elementwise positive solvent, elementwise negative |
| 강연 형태 (Language of Session (Talk)) |
English |