More properties of ( ss,gamma)-Chebyshev functions and points

Article Computer Science, Software Engineering

On Kosloff Tal-Ezer least-squares quadrature formulas

G. Cappellazzo et al.

Summary: In this study, a global quadrature scheme for analytic functions on compact intervals is explored using function values on quasi-uniform grids of quadrature nodes. The study goes beyond classical interpolatory quadrature by adjusting the polynomial approximant degree and applying mapping functions to improve the convergence and stability of the scheme. The combination of the Kosloff Tal-Ezer map and least-squares approximation (KTL) for numerical quadrature is investigated, and its properties and computational implementation are discussed.

BIT NUMERICAL MATHEMATICS (2023)

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Article Mathematics

On (β, γ)-Chebyshev functions and points of the interval

Stefano De Marchi et al.

Summary: This paper introduces the class of (beta, gamma)-Chebyshev functions and corresponding points, proving their orthogonality in certain subintervals. It investigates the cases where they become polynomials and shows their relationship with classical Chebyshev polynomials. Additionally, subsets of Chebyshev and Chebyshev-Lobatto points are instances of (beta, gamma)-Chebyshev points, and the behavior of Lebesgue constants at these points is studied by varying the parameters beta and gamma.

JOURNAL OF APPROXIMATION THEORY (2021)

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Article Mathematics, Applied

Stable discontinuous mapped bases: the Gibbs-Runge-Avoiding Stable Polynomial Approximation (GRASPA) method

S. De Marchi et al.

Summary: The Fake Nodes Approach allows for changing the set of nodes without the need for resampling the function, and has been successfully applied to mitigate the Runge's phenomenon and the Gibbs phenomenon. The GRASPA approach offers a new way to simultaneously mitigate both the Runge's and Gibbs phenomena.

COMPUTATIONAL & APPLIED MATHEMATICS (2021)

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Article Mathematics, Applied