컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0520 |
|---|---|
| 분류(Section) | Poster Session |
| 분과(Session) | Numerical Analysis / Scientific Computations / Mathematics in Science and Technology (SS-14) |
| 영문제목 (Title(Eng.)) |
On simple algorithm approximating arbitrary real powers $A^{\alpha}$ of a matrix from number representation system |
| 저자(Author(s)) |
Jong-Hyeon Seo1 Pusan National University1 |
| 초록본문(Abstract) | In this paper we present new algorithm for approximating arbitrary real powers A^{\alpha} of a matrix A\in\mathbb{C}^{n\times n} only using matrix standard operation and matrix square root algorithms. So it has flexible accuracy, efficicency and stablilty. That is if one wants more stable algorithm then this algorithm is and if other needs getting an inaccurate solution in efficient way then also does only by changing the matrix square root algorithms. Furthermore if a real matrix with no real negative eigenvalues is given then we get real solution without complex arithmetic and its accuracy is only depend on a condition nubmer of A and that of matrix roots. Since the new algorithm works for arbitrary real \alpha and is independent on singularity and defectiveness agianst Pade approximation and Schur-Parllet algorithm repectively, it seems the only way to get a good approximation of arbitrary real power without any handling when a given marix has such conditions. To addition this algorithm is also well suited in parrellel computation because it can be implemented only by standard matrix operations. |
| 분류기호 (MSC number(s)) |
65F30 |
| 키워드(Keyword(s)) | matrix real power, matrix p-th root, real matrix p-th root, matrix square root, generalization of matrix binary powering, circular binary decimal number representation, number representation syste |
| 강연 형태 (Language of Session (Talk)) |
English |