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Explicit forms of interpolating cubic splines and data smoothing

Author

Listed:
  • Török, Csaba
  • Hudák, Juraj
  • Pristaš, Viktor
  • Antoni, Lubomir

Abstract

We express the interpolating cubic splines of class C2 in their new, explicit forms. We construct the desired forms, the spline's Hermitian and B-spline representations for both equidistant and arbitrary nodes. During this process we demonstrate an innovative way to compute the inverse of a special class of tridiagonal matrices. Afterward, we propose the corresponding interpolating spline based linear regression models with easily interpretable coefficients suitable for smoothing data of complex structures.

Suggested Citation

  • Török, Csaba & Hudák, Juraj & Pristaš, Viktor & Antoni, Lubomir, 2025. "Explicit forms of interpolating cubic splines and data smoothing," Applied Mathematics and Computation, Elsevier, vol. 500(C).
    • Handle: RePEc:eee:apmaco:v:500:y:2025:i:c:s0096300325001389
    DOI: 10.1016/j.amc.2025.129411
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