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Least squares piecewise cubic curve fitting

Published:01 June 1973Publication History
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Abstract

The matrices involved in a linear least squares formulation are determined for the problem of fitting piecewise cubic functions, those possessing a continuous derivative, to arrays of planar data.

References

  1. 1 Ferguson, J. Least squares 'spline' curve fitting. TRW Applied Math. Report 3122-11, Feb. 18, 1966.Google ScholarGoogle Scholar
  2. 2 Barrodale, I., and Young A. A note on numerical procedures for approximation by spline functions. Computer J. 9 (Nov. 1966), 318-320.Google ScholarGoogle ScholarCross RefCross Ref
  3. 3 Reinsch, C.H. Smoothing by spline functions. Num. Math. 10 (1967), 177-183.Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 4 Curtis, A.R., and Powell, M.J.D. Using cubic splines to approximate functions of one variable to prescribed accuracy. AERE-R 5602. Harwell, Berk, England, Nov. 1967.Google ScholarGoogle Scholar
  5. 5 Anselone, P.M., and Laurent, P.J. A general method for the construction of interpolating or smoothing spline functions. Num. Math. 12 (1968), 66--82.Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6 deBoor, C., and Rice, J.R. Least squares cubic spline approximation, I--Fixed Knots, II--Variable Knots. CSD TR20 and CSD TR21, Purdue U. Lafayette, Ind., Apr. 1968.Google ScholarGoogle Scholar
  7. 7 Greville, T.N.E. (Ed.) Theory and Applications of Spline Functions. Academic Press, New York, 1969.Google ScholarGoogle Scholar
  8. 8 Rivlin, T.J. An Introduction to the Approximation of Functions. Blaisddl Pub. Co., Waltham, Mass. 1969.Google ScholarGoogle Scholar
  9. 9 Harrison Jr, J.O. Piecewise polynomial approximation for large scale digital computers. Math. Tables Aids to Comp. 3 (1949), 400-407.Google ScholarGoogle Scholar
  10. 10 Stone, H. Approximation of curves by line segments. Math. 15 (1961), 40-47.Google ScholarGoogle Scholar
  11. 11 Hanson, R.J. Computing quadratic programming problems: linear inequality and equality constraints. Jet Propulsion Lab. Sec. 314, Tech. Memo No. 240, Feb. 9, 1970.Google ScholarGoogle Scholar

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        cover image Communications of the ACM
        Communications of the ACM  Volume 16, Issue 6
        June 1973
        60 pages
        ISSN:0001-0782
        EISSN:1557-7317
        DOI:10.1145/362248
        Issue’s Table of Contents

        Copyright © 1973 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 June 1973

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