Summary
The purpose of this paper is to develop complete spline smoothing methods from a computational point of view, culminating in efficient stable numerical algorithms. Both the univariate and bivariate (tensorproduct) cases will be treated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anselone, P.M., Laurent, P.J.: A general method for the construction of interpolating and smoothing spline functions. Numer. Math.12, 66–82 (1968)
Baszenski, G., L.L. Schumaker: The tensor-product scheme of Abstract smoothing splines. (To appear in Proc. Haar Memorial Conf., Budapest)
deBoor, C.: Efficient computer manipulation of tensor products. ACM Trans. Math. Softwere5, 173–182 (1979)
Dierckx, P.: An algorithm for surface fitting with spline functions. IMA J. Numer. Anal.1, 267–283 (1981)
Dierckx, P.: A fast algorithm for smoothing data on a rectangular grid while using splines. SIAM J. Numer. Anal.19, 1286–1304 (1982)
Dyn, N., G. Wahba: On the estimation of functions of several variables from aggregated data. SIAM J. Math. Anal.13, 134–152 (1982)
Franke, R.: A critical comparison of some methods for interpolation of scattered data. Rpt. NPS-53-79-003, Naval Postgraduate School, Monterey, CA: 1979
Hayes, J.G., Halliday, J.: The least-squares fitting of cubic spline surfaces to general date sets. J. Inst. Math. Appl.14, 89–103 (1974)
Hu, C., Schumaker, L.L.: Bivariate natural spline smoothing, in Delay Equations. Approximation and Application (G. Meinardus, G. Nurnberger, eds.) pp. 165–179. Basel: Birkhauser 1985
Larkin, F.M.: Optimal estimation of bounded linear functionals from noisy data. IFIP CongressTA-1-89–98 (1971)
Lyche, T., Schumaker, L.L.: Computation of smoothing and interpolating natural splines via local bases. SIAM J. Numer. Anal.10, 1027–1038 (1973)
Lyche, T., Sepehrnoori, K., Schumaker, L.L.: Fortran subroutines for computing smoothing and interpolating natural splines. Adv. Eng. Software5, 2–5 (1983)
Nielson, G.: Smoothing and interpolating splines. PhD dissertation, Univ. of Utah, 1972
Reinsch, C.H.: Smoothing by spline functions. Numer. Math.10, 177–183 (1967)
Reinsch, C.H.: Smoothing by spline functions II. Numer. Math.16, 451–454 (1971)
Schoenberg, I.J.: Spline functions and the problem of graduation. Proc. Natl. Acad. Sci. USA52, 947–950 (1964)
Schumaker, L.L.: Fitting surfces to scattered data. In: Approximation Theory II (G.G. Lorentz, C.K. Chui, L.L. Schumaker eds.), pp. 203–268. New York: Academic Press 1976
Schumaker, L.L.: Spline Functions: Basic Theory. New York: John Wiley 1981
Wahba, G., Wendelberger, J.: Some new mathematical methods for variational objective analysis using splines and cross-validation. Mon. Weather Rev.108, 1122–1143 (1980)
Woodford, C.H.: An algorithm for data smoothing using spline functions. BIT10, 501–510 (1971)
Author information
Authors and Affiliations
Additional information
Supported in part by NASA Contract NAS9-16664
Rights and permissions
About this article
Cite this article
Hu, C.L., Schumaker, L.L. Complete spline smoothing. Numer. Math. 49, 1–10 (1986). https://doi.org/10.1007/BF01389426
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01389426