컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0587 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Numerical Analysis / Scientific Computations / Mathematics in Science and Technology (SS-14) |
| 영문제목 (Title(Eng.)) |
Finding special solvents to some nonlinear matrix equations by Newton's method |
| 저자(Author(s)) |
Yin-Huan Han1 School of Mathematics and Physics, Qingdao University of Science and Technology , Qingdao, P.R.China1 |
| 초록본문(Abstract) | One of our interesting nonlinear matrix equations is the quadratic matrix equation which can be defined by $$ Q(X) = AX^2 + BX + C = 0, $$ where $X$ is an $n\times n$ unknown real matrix and $A$, $B$ and $C$ are $n \times n$ given matrices with real elements. Another one is the matrix polynomial \begin{equation*} P(X)=A_0X^m+A_1X^{m-1}+\cdots+A_m=0, \qquad X, A_i\in\mathbb{R}^{n\times n}. \end{equation*} Newton's method is used to find the symmetric, bisymmetric, centro symmetric and skew symmetric solvents of the nonlinear matrix equations $Q(X)$ and $P(X)$. We also show that our algorithms converge the special solvents even if the Fr\'{e}chet derivatives are singular. Finally, we give some numerical examples. |
| 분류기호 (MSC number(s)) |
65F30 |
| 키워드(Keyword(s)) | quadratic matrix equation, matrix polynomial, Fr\'{e}chet derivative, quadratic eigenvalue problems, bisymmetric, centro symmetric, skew symmetric |
| 강연 형태 (Language of Session (Talk)) |
English |