Bivariate natural spline smoothing. (English) Zbl 0561.41011

Hu, Chui Li; Schumaker, Larry L.

Delay equations, approximation and application, Int. Symp. Mannheim/Ger. 1984, ISNM 74, 165-179 (1985).

[For the entire collection see Zbl 0554.00008.]
This paper deals with the problem of smoothing data given on a rectangular grid. More specifically, the authors discuss an efficient algorithm for calculating the well-known bivariate natural splines which minimize a combination of smoothness and goodness of fit, or which minimize smoothness subject to some prescribed goodness of fit. The algorithms are based on a representation using tensor-products of univariate natural B-splines. It is shown that that first problem leads to a convenient linear system of equations of a special tensor form which can be very efficiently solved. The second problem is solved by computing a sequence of solutions of the first problem in an iterative process which adjusts the weight between the measure of smoothness and the measure of goodness of fit.

MSC:

41A15

Spline approximation

Keywords:

smoothing data; algorithm; bivariate natural splines; tensor-products

Citations:

Zbl 0554.00008