Explicit forms of interpolating cubic splines and data smoothing

Csaba Török, Juraj Hudák, Viktor Pristaš and Lubomir Antoni

Applied Mathematics and Computation, 2025, vol. 500, issue C

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.

Keywords: Data smoothing; Cubic splines; Interpolation; Linear regression (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:500:y:2025:i:c:s0096300325001389

DOI: 10.1016/j.amc.2025.129411

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