Projection approximation functionals for minimal splines

E. K. Kulikov, A. A. Makarov

Saint Petersburg State University

Abstract: In this paper, formulas of approximation functionals of projection type for quadratic minimal splines are constructed. The values of these functionals are then used as coefficients in local approximation schemes. Examples of special cases of the resulting approximation structures, known to have quasi-interpolation nature, are given. Results of numerical experiments on approximating transcendental curves using the proposed local scheme are presented, and a numerical method for solving integral equations using projection functionals is developed.

Key words and phrases: B-splines, minimal splines, local approximation, quasi-interpolation, Fredholm integral equations.

UDC: 519.6

Received: 05.10.2025