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| Presentation | 2013-10-29 15:30 A note on systematic construction of omega-matrices Norikazu Takahashi (Okayama Univ.), Tetsuo Nishi (Waseda Univ.)  NLP2013-106 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | In 1991, Nishi and Kawane introduced the notion of $Omega$-matrix in their analysis of DC operating points of nonlinear circuits containing transistors. As a generalization of $P_0$-matrices which are well known in circuit theory and matrix theory, $Omega$-matrices have many interesting properties. However, no systematic way of constructing $Omega$-matrices is known so far. This may be because the mathematical structure of $Omega$-matrices is rather complicated. In this report, we give two simple methods for constructing $Omega$-matrices that are not $P_0$-matrices. In the first method, all entries in the first row are set to negative values, all entries in the first column and the diagonal line below the first row are set to positive values, and all other entries are set to zero. Here, we should note that only the sign is important for each entry and its absolute value is arbitrary. In the second method, we first construct a matrix by the first method under the condition that the absolute value of each diagonal entry is sufficiently small. Then, by computing the inverse of the matrix, we can obtain an $Omega$-matrix. The first method generates sparse $Omega$-matrices, while the second one generates dense $Omega$-matrices. | |
| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | nonlinear equation / the number of solutions / $Omega$-matrix / $P_0$-matrix / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 113, no. 271, NLP2013-106, pp. 193-198, Oct. 2013. | |
| Paper # | NLP2013-106 | |
| Date of Issue | 2013-10-21 (NLP) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | NLP2013-106 |
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| Conference Information | |
| Committee | NLP |
| Conference Date | 2013-10-28 - 2013-10-29 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Sanport Hall Takamatsu |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | General |
| Paper Information | |
| Registration To | NLP |
| Conference Code | 2013-10-NLP |
| Language | Japanese |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A note on systematic construction of omega-matrices |
| Sub Title (in English) | |
| Keyword(1) | nonlinear equation |
| Keyword(2) | the number of solutions |
| Keyword(3) | $Omega$-matrix |
| Keyword(4) | $P_0$-matrix |
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| 1st Author's Name | Norikazu Takahashi |
| 1st Author's Affiliation | Okayama University (Okayama Univ.) |
| 2nd Author's Name | Tetsuo Nishi |
| 2nd Author's Affiliation | Waseda University (Waseda Univ.) |
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| Speaker | Author-1 |
| Date Time | 2013-10-29 15:30:00 |
| Presentation Time | 15 minutes |
| Registration for | NLP |
| Paper # | NLP2013-106 |
| Volume (vol) | vol.113 |
| Number (no) | no.271 |
| Page | pp.193-198 |
| #Pages | 6 |
| Date of Issue | 2013-10-21 (NLP) |
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