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The iterative solution for smoothing with a cubic spline function. (English) Zbl 0679.65005

Numerical analysis, Proc. Int. Symp., Ankara/Turk. 1987, 153-165 (1989).
[For the entire collection see Zbl 0664.00023.]
The authors investigate interpolation and smoothing of given data by natural cubic splines. Solving this problem leads to a system of linear equations, where the coefficient matrix has a positive definite symmetric part. This system can be solved by applying the underrelaxed successive overrelaxation (SOR) method.
The authors describe some disadvantages of the SOR approach and, instead, apply the Lanczos method. This method yields the solution in a finite number of steps, in the absence of rounding errors, and does not require any estimation of parameters. The numerical results show that in certain cases the Lanczos method is faster than the SOR method.
Reviewer: G.Nürnberger

MSC:

65D10 Numerical smoothing, curve fitting
65D05 Numerical interpolation
65D07 Numerical computation using splines
65F10 Iterative numerical methods for linear systems

Citations:

Zbl 0664.00023