Brauer and Geršgorin Locations of Zeros of Perturbed Chebyshev Polynomials of the Second Kind by Translation
摘要
We consider some perturbed Chebyshev polynomials of the second kind obtained by modifying by translation one of its recurrence coefficients at an arbitrary order. By applying Brauer and Geršgorin theorems to Jacobi matrices associated with such perturbed sequences, we obtain some locations of their zeros and also a refined location of one extremal zero.