Construction of an Algebraic-Hyperbolic Natural Tension Spline of Eighth Order
DOI:
https://doi.org/10.71310/pcam.3_67.2025.06Keywords:
Hilbert space, generalized spline, algebraic-hyperbolic spline, convolution, discrete analogueAbstract
This paper first demonstrates that an algebraic-hyperbolic spline of eighth order minimizes the norm within a Hilbert space framework. Subsequently, employing Sobolev’s method, which involves constructing a discrete analogue of the differential operator, the spline function is developed. Unknown coefficients of the spline are computed according to predefined smoothness criteria and boundary conditions. As a result, the constructed spline exhibits exceptional smoothness, enhances interpolation accuracy, and precisely reproduces hyperbolic functions, linear polynomials, and constants. The findings indicate that this approach is highly effective for applications requiring smooth interpolation and accurate modeling of physical phenomena. Additionally, incorporating tension parameters enables precise adjustment of the spline’s stiffness or flexibility.
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