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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Improved rounding for spline coefficients and knots

Authors: Eric Grosse and John D. Hobby
Journal: Math. Comp. 63 (1994), 175-194
MSC: Primary 65D07
MathSciNet review: 1240659
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Abstract: When representing the coefficients and knots of a spline using only small integers, independently rounding each infinite-precision value is not the best strategy. We show how to build an affine model for the error expanded about the optimal full-precision free-knot or parameterized spline, then use the Lovász basis reduction algorithm to select a better rounding. The technique could be used for other situations in which a quadratic error model can be computed.

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Keywords: Free-knot splines, parameterized splines, rounding, closest lattice point, compression
Article copyright: © Copyright 1994 American Mathematical Society