Adduchi, Jim and Djakov, Plamen Borissov and Mityagin, Boris Samuel (2010) Convergence radii for eigenvalues of tridiagonal matrices. Letters in Mathematical Physics, 91 (1). pp. 4560. ISSN 03779017 (Print) 15730530 (Online)
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Official URL: http://dx.doi.org/10.1007/s1100500903668
Abstract
Consider a family of infinite tridiagonal matrices of the form L + zB, where the matrix L is diagonal with entries Lkk = k(2), and the matrix B is offdiagonal, with nonzero entries Bk,Bk+1 = Bk+1,Bk = k(alpha), 0 <=alpha <= 2. The spectrum of L + zB is discrete. For small vertical bar z vertical bar the nth eigenvalue En(z), En(0)=n(2), is a welldefined analytic function. Let Rn be the convergence radius of its Taylor's series about z=0. It is proved that
Rn <= C(alpha)n(2alpha) if 0 <=alpha<11/6.
Item Type:  Article 

Uncontrolled Keywords:  tridiagonal matrix; operator family; eigenvalues 
Subjects:  Q Science > QA Mathematics > QA299.6433 Analysis 
Divisions:  Faculty of Engineering and Natural Sciences 
Depositing User:  Plamen Borissov Djakov 
Date Deposited:  11 Mar 2010 10:48 
Last Modified:  26 Apr 2022 08:36 
URI:  https://research.sabanciuniv.edu/id/eprint/13811 
Available Versions of this Item

Convergence Radii for Eigenvalues of tridiagonal matrices. (deposited 04 Nov 2009 21:32)
 Convergence radii for eigenvalues of tridiagonal matrices. (deposited 11 Mar 2010 10:48) [Currently Displayed]