Tridiagonal test matrices for eigenvalue computations: Two-parameter extensions of the Clement matrix

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• 作者：Roy Oste ; ^{Roy.Oste@UGent.be} ; Joris Van der Jeugt ^{Joris.VanderJeugt@UGent.be}
• 关键词：65F15 ; 15A18 ; 15A36
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：314
• 期：Complete
• 页码：30-39
• 全文大小：874 K
• 卷排序：314

文摘

The Clement or Sylvester–Kac matrix is a tridiagonal matrix with zero diagonal and simple integer entries. Its spectrum is known explicitly and consists of integers which makes it a useful test matrix for numerical eigenvalue computations. We consider a new class of appealing two-parameter extensions of this matrix which have the same simple structure and whose eigenvalues are also given explicitly by a simple closed form expression. The aim of this paper is to present in an accessible form these new matrices and examine some numerical results regarding the use of these extensions as test matrices for numerical eigenvalue computations.