2013 Fiscal Year Final Research Report
Generation of extremely ill-conditioned matrices and illconditoned circuits
| Project/Area Number |
23560472
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Communication/Network engineering
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| Research Institution | Waseda University |
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Principal Investigator |
NISHI TETSUO 早稲田大学, 理工学術院, 招聘研究員 (40037908)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKAHASHI Norikazu 岡山大学, 大学院自然科学研究科, 教授 (60284551)
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| Project Period (FY) |
2011 – 2013
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| Keywords | たちの悪い行列の生成 / 行列の条件数 / 非線形方程式 / 解の個数 / Ω行列 / アダマール行列 |
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| Research Abstract |
The quality of numerical algorithms can be evaluated by solving extremely ill-conditioned problems; For example, linear simultaneous equations having a coefficient matrix with extremely large condition number and nonlinear equations possessing infinitely many solutions. For this purpose we studied on the generation of extremely ill-conditioned matrices and on an upper bound of the condition number of a matrix and showed the possibility that the upper bound of the condition number derived by Guggenheimer, et al may approximately be achieved.
We also investigate a nonlinear equation derived originally from transistor circuits and found some interesting properties of solution curve equations derived from it.
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