## Convergence radii for eigenvalues of tri-diagonal matricesAdduchi, Jim and Djakov, Plamen Borissov and Mityagin, Boris Samuel (2010)
Official URL: http://dx.doi.org/10.1007/s11005-009-0366-8 ## AbstractConsider 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- Convergence Radii for Eigenvalues of tri--diagonal matrices. (deposited 04 Nov 2009 21:32)
- Convergence radii for eigenvalues of tri-diagonal matrices. (deposited 11 Mar 2010 10:48)
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- Convergence radii for eigenvalues of tri-diagonal matrices. (deposited 11 Mar 2010 10:48)
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