Practical spline approximation
This two-part paper describes the use of polynomial spline functions for purposes of interpolation and approximation. The emphasis is on practical utility rather than detailed theory. Part I introduces polynomial splines, defines B-splines and treats the representation of splines in terms of B-splines. Part II deals with the statement and solution of spline interpolation and least squares spline approximation problems. It also discusses strategies for selecting particular solutions to spline approximation problems having nonunique solutions and techniques for automatic knot placement.
KeywordsSpline Interpolation Divided Difference Polynomial Spline Triangular System Rank Deficiency
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- COX, M.G. 1975a Numerical methods for the interpolation and approximation of data by spline functions. London, City University, PhD Thesis.Google Scholar
- COX, M.G. 1976 A survey of numerical methods for data and function approximation. The State of the Art in Numerical Analysis, D.A.H. Jacobs, Ed., London, Academic Press, 627–668.Google Scholar
- COX, M.G. 1978a The representation of polynomials in terms of B-splines. Proc. Seventh Manitoba Conference on Numerical Mathematics and Computing, D. McCarthy and H.C. Williams, Eds., Winnepeg, University of Manitoba, 73–105.Google Scholar
- COX, M.G. 1978b The incorporation of boundary conditions in spline approximation problems. Lecture Notes in Mathematics 630: Numerical Analysis, G.A. Watson, Ed., Berlin, Springer-Verlag, 51–63.Google Scholar
- DE BOOR, C. 1974 Good approximation by splines with variable knots II. Lecture Notes in Mathematics 363: Numerical Solution of Differential Equations, G.A. Watson, Ed., Berlin, Springer-Verlag, 12–20.Google Scholar
- DE BOOR, C. and RICE, J.R. 1968 Least squares cubic spline approximation II — variable knots. Purdue University Report No. CSD TR 21.Google Scholar
- HAYES, J.G. 1978 Data-fitting algorithms available, in preparation, and in prospect, for the NAG Library. Numerical Software-Needs and Availability, D.A.H. Jacobs, Ed., London, Academic Press.Google Scholar
- KOZAK, J. 1980 On the choice of the exterior knots in the B-spline basis for a spline space. University of Wisconsin Report 2148.Google Scholar
- POWELL, M.J.D. 1970 Curve fitting by splines in one variable. Numerical Approximation to Functions and Data, J.G. Hayes, Ed., London, Athlone Press, 65–83.Google Scholar
- RICE, J.R. 1969 The Approximation of Functions, Vol. II: Advanced Topics, Reading, Mass., Addison-Wesley.Google Scholar
- SCHOENBERG, I.J. and WHITNEY, Anne 1953 On Pólya frequency functions III. Trans. Am. Math. Soc. 74, 246–259.Google Scholar