We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant coefficients, can be orthogonal polynomial sequences. 1. Introduction The classical orthogonal polynom...

A polynomial filtered Davidson-type algorithm is proposed for symmetric eigenproblems, in which the correction-equation of the Davidson approach is replaced by a polynomial filtering step. The new approach has better global convergence and robustness properties when compared with standard Davidson-type methods. The typical filter used in this paper is based on Chebyshev polynomials. The goal of...

We construct a commutative algebra Ax of difference operators in R, depending on p + 3 parameters which is diagonalized by the multivariable Racah polynomials Rp(n; x) considered by Tratnik [27]. It is shown that for specific values of the variables x = (x1, x2, . . . , xp) there is a hidden duality between n and x. Analytic continuation allows us to construct another commutative algebra An in ...

one of the water resources modeling requirements is sufficient knowledge of long-term series of meteorological and hydrological parameters. in this study the nearest neighbor resampling method presented by lall and sharma was developed. in the developed model, the knn regression was used for time series forecasting instead of local polynomial used in the developed algorithm by prairie. in this ...

We present sharp estimates for the degree and the height of the polynomials in the Nullstellensatz over the integer ring Z. The result improves previous work of P. Philippon, C. Berenstein and A. Yger, and T. Krick and L. M. Pardo. We also present degree and height estimates of intrinsic type, which depend mainly on the degree and the height of the input polynomial system. As an application we ...