Improved computation of cubic natural splines with equi-spaced knots

Author:
Malcolm A. MacLeod

Journal:
Math. Comp. **27** (1973), 107-109

MSC:
Primary 65D05

MathSciNet review:
0326982

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Abstract: An improved algorithm is given for the computation of the coefficients of the interpolating polynomials for cubic natural splines with equi-spaced knots. By solving the continuity equation recursively, a gain in computation efficiency is obtained and the requirement of previous techniques for exact computation is eliminated.

**[1]**J. H. Ahlberg, E. N. Nilson, and J. L. Walsh,*The theory of splines and their applications*, Academic Press, New York-London, 1967. MR**0239327****[2]**T. N. E. Greville,*Table for third-degree spline interpolation with equally spaced arguments*, Math. Comp.**24**(1970), 179–183. MR**0258238**, 10.1090/S0025-5718-1970-0258238-1**[3]**W. D. Hoskins,*Table for third-degree spline interpolation using equi-spaced knots*, Math. Comp.**25**(1971), 797–801. MR**0298873**, 10.1090/S0025-5718-1971-0298873-9**[4]**Francis B. Hildebrand,*Finite-difference equations and simulations*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1968. MR**0228185****[5]**Robert D. Richtmyer and K. W. Morton,*Difference methods for initial-value problems*, Second edition. Interscience Tracts in Pure and Applied Mathematics, No. 4, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR**0220455**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1973-0326982-6

Keywords:
Natural spline interpolation,
smoothest interpolating function

Article copyright:
© Copyright 1973
American Mathematical Society