Ge´za Freud, orthogonal polynomials and Christoffel functions. A case study
Journal of Approximation Theory
Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
On the domain of convergence and poles of complex J - fractions
Journal of Approximation Theory
Journal of Approximation Theory
Fat Diagonals and Fourier Analysis
SIAM Journal on Matrix Analysis and Applications
From Toeplitz matrix sequences to zero distribution of orthogonal polynomials
Contemporary mathematics
Stability of the notion of approximating class of sequences and applications
Journal of Computational and Applied Mathematics
Spectral Features and Asymptotic Properties for $g$-Circulants and $g$-Toeplitz Sequences
SIAM Journal on Matrix Analysis and Applications
A note on the (regularizing) preconditioning of g-Toeplitz sequences via g-circulants
Journal of Computational and Applied Mathematics
Analysis of Multigrid Preconditioning for Implicit PDE Solvers for Degenerate Parabolic Equations
SIAM Journal on Matrix Analysis and Applications
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Under the mild trace-norm assumptions, we show that the eigenvalues of an arbitrary (non-Hermitian) complex perturbation of a Jacobi matrix sequence (not necessarily real) are still distributed as the real-valued function 2cost on [0,@p] which characterizes the nonperturbed case. In this way the real interval [-2,2] is still a cluster for the asymptotic joint spectrum and, moreover, [-2,2] still attracts strongly (with infinite order) the perturbed matrix sequence. The results follow in a straightforward way from more general facts that we prove in an asymptotic linear algebra framework and are plainly generalized to the case of matrix-valued symbols, which arises when dealing with orthogonal polynomials with asymptotically periodic recurrence coefficients.