Mathematics

On the calculation of the coefficients of cubic splines on a set of equidistant knots

A. A. Manukian

Yerevan State University, Faculty of Mathematics and Mechanics

Abstract: As is known, the coefficients of the interpolation cubic spline are found by solving a tridiagonal system of linear algebraic equations of a special type. To solve the system, a well-known numerical algorithm is usually used. In this paper, an alternative method for finding the coefficients of a natural cubic spline on a uniform set of knots is proposed. The method is based on the analytical inversion of the tridiagonal matrix, which made it possible to obtain closed-form expressions for the coefficients. This approach allows us both identify the analytical dependence of the spline coefficients on its values at the knots and obtain simple formulas for calculating these coefficients, by passing the solution of the system.

Keywords: cubic spline, tridiagonal matrix, inverse matrix

MSC: 65D07, 65F05

Received: 03.10.2025
Revised: 03.10.2025
Accepted: 12.12.2025

Language: English

DOI: 10.46991/PYSU:A.2025.59.2.063