On an Interpolation of a Function by Natural Splines
DOI:
https://doi.org/10.71310/pcam.3_67.2025.08Keywords:
Hilbert space, extremal function, error functional, spline functionAbstract
There are algebraic and variational approaches of construction in the spline theory. In algebraic approach splines are considered as some smooth piecewise polynomial functions. In the variational approach splines are elements of Hilbert or Banach spaces minimizing certain functionals. Then we study the problems of existence, uniqueness, and convergence of splines and algorithms for constructing them based on their own properties of splines. In this paper, we study the problem of natural spline functions in a Hilbert space. Here, using the Sobolev method, an algorithm is given for solving a system of linear algebraic equations for the coefficients of the natural spline functions. For ???? = 2, explicit expressions for the optimal coefficients of the natural spline function in the Hilbert space ????(2,0) are obtained.
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