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2013 Fiscal Year Final Research Report

Generation of extremely ill-conditioned matrices and illconditoned circuits

Research Project

  • PDF
Project/Area Number 23560472
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Communication/Network engineering
Research InstitutionWaseda University

Principal Investigator

NISHI TETSUO  早稲田大学, 理工学術院, 招聘研究員 (40037908)

Co-Investigator(Renkei-kenkyūsha) TAKAHASHI Norikazu  岡山大学, 大学院自然科学研究科, 教授 (60284551)
Project Period (FY) 2011 – 2013
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
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.

  • Research Products

    (13 results)

All 2014 2013 2012 2011

All Journal Article (4 results) (of which Peer Reviewed: 4 results) Presentation (9 results)

  • [Journal Article] Ex plicit proof of an inequality related to the Omega matrix2013

    • Author(s)
      T. Nishi, S. Oishi, N. Takahashi
    • Journal Title

      Nonlinear The- ory and Its Applications, IEICE

      Volume: vol.4, no.4 Pages: 430-450

    • DOI

      10.1587/nolta.4.430

    • Peer Reviewed
  • [Journal Article] 非線形方程式の解の個数・解曲線とΩ行列の役割2013

    • Author(s)
      西哲生
    • Journal Title

      Fundamental Review

      Volume: vol. 7, no. 2 Pages: 103–115

    • URL

      https://www.jstage.jst.go.jp/article/essfr/7/2/7_103/_pdf

    • Peer Reviewed
  • [Journal Article] Some properties of solution curves of a class of nonlinear equations and the number of solutions2012

    • Author(s)
      T. Nishi, S. Oishi and N. Takahashi
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: Vol. 3 (2012) No. 3 Pages: 301-335

    • DOI

      10.1588/nolta.3.301

    • Peer Reviewed
  • [Journal Article] On the generation of very illconditioned integer matrices2011

    • Author(s)
      T. Nishi, S. Rump, and S. Oishi
    • Journal Title

      Nonlinear Theory and Its Appl

      Volume: IEICE Vol. 2, No. 2 Pages: 226-245

    • DOI

      10.1588/nolta.2.226

    • Peer Reviewed
  • [Presentation] 行列の条件数の最大値に関する考察2014

    • Author(s)
      西哲生, S. Rump,高橋規一
    • Organizer
      IEICE NLP Tech. Rept
    • Place of Presentation
      上智大学(NLP2013-179)
    • Year and Date
      20140300
  • [Presentation] A consideration on the condition number of extremely ill conditioned matrices2013

    • Author(s)
      T. Nishi, S. Rump, S. Oishi
    • Organizer
      Proc. 2013 Eu- ropean Conference on Circuit Theory and Appl
    • Place of Presentation
      Dresden, Germany
    • Year and Date
      20130908-12
  • [Presentation] Generation of illconditioned matrices of order n2013

    • Author(s)
      T. Nishi, S. Rump, S. Oishi
    • Organizer
      IE- ICE NLP Tech. Rept
    • Place of Presentation
      中京大学(NLP2013-8)
    • Year and Date
      20130400
  • [Presentation] Q行列の系統的構成法に関する一考察2013

    • Author(s)
      高橋規一,西哲生
    • Organizer
      IEICE NLP Tech. Rept
    • Place of Presentation
      サンポートホール高松(NLP2013-106)
    • Year and Date
      20130300
  • [Presentation] A consid- eration on the generation of extremely ill conditioned matrices2013

    • Author(s)
      T. Nishi, S. Rump, S. Oishi
    • Organizer
      IEICE NLP Tech. Rept
    • Place of Presentation
      千葉大学(NLP2012-149)
    • Year and Date
      20130300
  • [Presentation] A the orem on a solution curve of a class of nonlinear equations2012

    • Author(s)
      T. Nishi, S. Oishi, N. Takahashi
    • Organizer
      Proc. 2012 Inter- nat'l Symp. on Nonlinear Theory and its Appl
    • Place of Presentation
      Palma, Majorca, Spain(NOLTA2012)
    • Year and Date
      20121022-26
  • [Presentation] Proof of an inequality related to the Omega matrix2012

    • Author(s)
      T. Nishi, S. Oishi, N. Takahashi
    • Organizer
      IEICE CAS & NLP Tech. Rept
    • Place of Presentation
      高知県立大学(CAS2012- 42 & NLP2012-68)
    • Year and Date
      20120900
  • [Presentation] Some properties of extremal points of solution curves for a class of nonlinear equations2012

    • Author(s)
      T. Nishi, S. Oishi, N. Takahashi
    • Organizer
      IEICE NLP Tech. Rept
    • Place of Presentation
      鹿児島県産業会館(NLP2012-52)
    • Year and Date
      20120700
  • [Presentation] On the Rank of a Jacobian Matrix of a Class of Non linear Equations2012

    • Author(s)
      T. Nishi, S. Oishi, N. Takahashi
    • Organizer
      IEICE CAS Tech. Rept
    • Place of Presentation
      新潟大学駅南キャンパス(CAS2011-127)
    • Year and Date
      20120300

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Published: 2015-07-16  

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