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A study on validated computation of zeros of analytic functions
http://hdl.handle.net/2241/6364
http://hdl.handle.net/2241/63642f52e54f-10d2-4c82-a3ba-aade66ce5b48
Item type | Thesis or Dissertation(1) | |||||
---|---|---|---|---|---|---|
公開日 | 2007-07-25 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | A study on validated computation of zeros of analytic functions | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_db06 | |||||
タイプ | doctoral thesis | |||||
アクセス権 | ||||||
アクセス権 | open access | |||||
アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||
著者 |
牛, 暁明
× 牛, 暁明 |
|||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | In this thesis, we consider the problem of computing the zeros of analytic functions that lie inside a circular region of the complex plane. A validated method for bounding cluster of zeros of analytic functions and a validated method for locating the zeros in the cluster are proposed. First we consider the problem of computing the zeros of polynomials which have multiple zeros or clusters of zeros. An eigenvalue method is presented which consructs a new companion matrix whose eigenvalues are simple and the zeros of given polynomial. This method can caluculate multiple zeros and their mltiplicities accurately, and it is also efficient in calculating the center of the cluster of zeros and the number of zeros in the cluster. One problem in computing zeros of polynomials using eigenvalue method is that a small pertubation in the elements of a companion matrix may produce significant changes in the eigenvalues of the companion matrix calculated by the QR method. ・・・ | |||||
言語 | en | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | Includes bibliographical references | |||||
言語 | en | |||||
書誌情報 |
発行日 2004 |
|||||
取得学位 | ||||||
学位名 | 博士(工学) | |||||
取得学位 | ||||||
学位名 | Doctor of Philosophy in Engineering | |||||
学位授与大学 | ||||||
学位授与機関識別子Scheme | kakenhi | |||||
学位授与機関識別子 | 12102 | |||||
言語 | ja | |||||
学位授与機関名 | 筑波大学 | |||||
言語 | en | |||||
学位授与機関名 | University of Tsukuba | |||||
学位授与年度 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 2003 | |||||
学位授与年月日 | ||||||
学位授与年月日 | 2004-03-25 | |||||
報告番号 | ||||||
学位授与番号 | 甲第3426号 |