Geno Nikolov

collaborators

4 papers

math.NA2026

On the error bounds of the Gauss-type quadrature formulae associated with spaces of parabolic and cubic spline functions with double equidistant knots

Geno Nikolov, Petar B. Nikolov

In two papers from 1995 P. Köhler and G. Nikolov showed that Gauss--type quadrature formulae associated with spaces of spline functions with equidistant knots are asymptotically op…

math.CA2026

An inequality for Jacobi polynomials: a complement to Finite Increment Theorem

Geno Nikolov

Let $P = P_{n}^{(α, β)}$ be the $n$ -th degree Jacobi polynomial, which is orthogonal in $[- 1, 1]$ with respect to the weight function $(1 - x)^{α} (1 + x)^{β}$ , $α, β > - 1$ . For parameters $(α, β)$ s…

math.CA2024

Simple bounds for the extreme zeroes of Jacobi polynomials

Geno Nikolov

Some new bounds for the extreme zeroes of Jacobi polynomials are obtained with an elementary approach. A feature of these bounds is their simple forms, which make them easy to work…

math.NA2024

Modified Trapezoidal Product Cubature Rules. Definiteness, Monotonicity and a Posteriori Error Estimates

Geno Nikolov, Petar Nikolov

We study two modifications of the trapezoidal product cubature formulae, approximating double integrals over the square domain $[a, b]^{2} = [a, b] \times [a, b]$ . Our modified cubature fo…