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- W2073608468 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. Introduction. Considerable interest has developed over the last several years in the use of spline functions for interpolation, largely as a result of the discovery of their extremal properties (1). Cubic splines have become popular because they combine a fair degree of approximation (continuity of the function and its first two derivatives at the knots) with relative ease of determination of the spline parameters (only a second-order difference equation need be solved). Two recent papers have shown that the parameters may be even more simply determined for the case of natural splines defined at equi-spaced knots ((2), (3)). Unfortunately, the techniques given in both these papers suffer from the defect that they require exact computation. To retain any accuracy requires multiple precision computation once the number of data points exceeds the limiting value nL = (n8/log 4) - 2, where n8 is the number of significant decimal digits carried by the computer employed. In the present paper, an improved algorithm is presented which does not require exact computation and which also displays an improved efficiency in determining the spline parameters." @default.
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- W2073608468 date "1973-01-01" @default.
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- W2073608468 title "Improved computation of cubic natural splines with equi-spaced knots" @default.
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- W2073608468 doi "https://doi.org/10.1090/s0025-5718-1973-0326982-6" @default.
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