Convergence radii for eigenvalues of tri-diagonal matrices
Adduchi, Jim and Djakov, Plamen Borissov and Mityagin, Boris Samuel (2010) Convergence radii for eigenvalues of tri-diagonal matrices. Letters in Mathematical Physics, 91 (1). pp. 45-60. ISSN 0377-9017 (Print) 1573-0530 (Online)
This is the latest version of this item.
Official URL: http://dx.doi.org/10.1007/s11005-009-0366-8
Consider a family of infinite tri-diagonal matrices of the form L + zB, where the matrix L is diagonal with entries L-kk = k(2), and the matrix B is off-diagonal, with non-zero entries B-k,B-k+1 = B-k+1,B-k = k(alpha), 0 <=alpha <= 2. The spectrum of L + zB is discrete. For small vertical bar z vertical bar the nth eigenvalue E-n(z), E-n(0)=n(2), is a well-defined analytic function. Let R-n be the convergence radius of its Taylor's series about z=0. It is proved that R-n <= C(alpha)n(2-alpha) if 0 <=alpha<11/6.
Available Versions of this Item
Repository Staff Only: item control page