Date of this Version
P. Z. Revesz, Cubic spline interpolation by solving a recurrence equation instead of a tridiagonal matrix, Proc. 1st International Conference on Mathematical Methods and Computational Techniques in Science and Engineering, WSEAS Press, pp. 21-25, Athens, Greece, November 2014.
The cubic spline interpolation method is proba- bly the most widely-used polynomial interpolation method for functions of one variable. However, the cubic spline method requires solving a tridiagonal matrix-vector equation with an O(n) computational time complexity where n is the number of data measurements. Even an O(n) time complexity may be too much in some time-ciritical applications, such as continuously estimating and updating the flight paths of moving objects. This paper shows that under certain boundary conditions the tridiagonal matrix solving step of the cubic spline method could be entirely eliminated and instead the coefficients of the unknown cubic polynomials can be found by solving a single recurrence equation in much faster time.