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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2024 MCQ for Mathematics of Computation is 1.78.

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An unconditionally convergent method for computing zeros of splines and polynomials
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by Knut Mørken and Martin Reimers;
Math. Comp. 76 (2007), 845-865
DOI: https://doi.org/10.1090/S0025-5718-07-01923-0
Published electronically: January 9, 2007

Abstract:

We present a simple and efficient method for computing zeros of spline functions. The method exploits the close relationship between a spline and its control polygon and is based on repeated knot insertion. Like Newton’s method it is quadratically convergent, but the new method overcomes the principal problem with Newton’s method in that it always converges and no starting value needs to be supplied by the user.
References
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  • T. Lyche and K. Mørken. Spline Methods, draft. Deparment of Informatics, University of Oslo, http://heim.ifi.uio.no/˜knutm/komp04.pdf, 2004.
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Bibliographic Information
  • Knut Mørken
  • Affiliation: Department of Informatics and Center of Mathematics for Applications, P.O. Box 1053, Blindern, 0316 Oslo, Norway
  • Email: knutm@ifi.uio.no
  • Martin Reimers
  • Affiliation: Center of Mathematics for Applications, P.O. Box 1053, Blindern, 0316 Oslo, Norway
  • Email: martinre@ifi.uio.no
  • Received by editor(s): April 1, 2005
  • Received by editor(s) in revised form: November 27, 2005
  • Published electronically: January 9, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 76 (2007), 845-865
  • MSC (2000): Primary 41A15, 65D07, 65H05
  • DOI: https://doi.org/10.1090/S0025-5718-07-01923-0
  • MathSciNet review: 2291839