On Numerical Computation of the Spectrum of a Class of Convolution Operators Related to Delay Systems

• HIRATA Kentaro

  Graduate School of Information Science, Nara Institute of Science and Technology

Bibliographic Information

Other Title

• 時間遅れシステムに関連したある種のたたみ込み積分作用素のスペクトルの数値計算について
• ジカン オクレ システム ニ カンレンシタ アルシュ ノ タタミコミ セキブン サヨウソ ノ スペクトル ノ スウチ ケイサン ニ ツイテ

Abstract

A class of convolution operators on fixed interval with initial values is considered. The numerical computation of its spectra is attempted via a finite-dimensional approximation so-called fast sampling and hold. In contrast to the case of matrices, the spectrum of an operator is not continuous against small perturbations in general. This implies that a fine approximation does not necessarily lead to better estimates close to the true values. Therefore, one must provide a mathematical justification of the procedure depending on the operator of interest. In this paper, continuity of the spectrum of the convolution operator described above is proved and a numerical computation formula for the calculation of its eigenvalues is given.

Journal

• Transactions of the Institute of Systems, Control and Information Engineers

  Transactions of the Institute of Systems, Control and Information Engineers 21 (3), 83-88, 2008

  THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)

Keywords

• convolution operator
• perturbation
• spectrum

Details

• CRID: 1390282680143238912
• NII Article ID: 10020503813
• NII Book ID: AN1013280X
• DOI: 10.5687/iscie.21.83
• ISSN: 2185811X
• ISSN: 13425668
• NDL BIB ID: 9415155
• Web Site: http://id.ndl.go.jp/bib/9415155
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I9415155
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed