Coefficients of Optimal Interpolation Formulas in the Hilbert Space of Differentiable Functions

• Published in: Lobachevskii journal of mathematics Vol. 46; no. 1; pp. 432 - 446
• Main Authors: Hayotov, A. R., Doniyorov, N. N.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.01.2025; Springer Nature B.V
• Subjects: Algebra; Analysis; Approximation; Boundary value problems; Fourier transforms; Geometry; Hilbert space; Integral equations; Interpolation; Mathematical functions; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Ordinary differential equations; Parametric equations; Polynomials; Probability Theory and Stochastic Processes; Trigonometric functions; error function; hypocycloid; differential equation; cycloid; epicycloid; optimal interpolation formula; Hilbert space; 2010 Mathematics Subject Classification: 41A05, 65D05, 65D10; extremal function; spline function
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S1995080224608130

In this work, we consider the problem of constructing optimal interpolation formulas and we get such formulas that are exact to trigonometric functions and , and algebraic polynomials of degree in the Hilbert space of differentiable functions. We obtain analytic formulas for the coefficients of the optimal interpolations formulas. In addition, we consider the problem of restoring curves given by parametric equations in the plane using optimal interpolation formulas.