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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Algorithms for piecewise polynomials and splines with free knots
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by G. Meinardus, G. Nürnberger, M. Sommer and H. Strauss PDF
Math. Comp. 53 (1989), 235-247 Request permission

Abstract:

We describe an algorithm for computing points $a = {x_0} < {x_1} < \cdots < {x_k} < {x_{k + 1}} = b$ which solve certain nonlinear systems $d({x_{i - 1}},{x_i}) = d({x_i},{x_{i + 1}})$, $i = 1, \ldots ,k$. In contrast to Newton-type methods, the algorithm converges when starting with arbitrary points. The method is applied to compute best piecewise polynomial approximations with free knots. The advantage is that in the starting phase only simple expressions have to be evaluated instead of computing best polynomial approximations. We finally discuss the relation to the computation of good spline approximations with free knots.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 235-247
  • MSC: Primary 65D07; Secondary 41A15
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0969492-7
  • MathSciNet review: 969492