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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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Hybrid spline frames
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by Say Song Goh, Tim N. T. Goodman and S. L. Lee PDF
Math. Comp. 78 (2009), 1537-1551 Request permission

Abstract:

Using their unitary extension principle, Ron and Shen have constructed a normalized tight frame for $L^2(\mathbb {R})$ consisting of spline functions with uniform knots. This paper constructs a normalized tight frame for $L^2((0,\infty ))$ comprising spline functions with knots on a hybrid of uniform and geometric mesh. The construction is motivated by applications in adaptive approximation using spline functions on a hybrid mesh that admits a natural dyadic multiresolution approximation of $L^2((0,\infty ))$ based on dilation and translation.
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Additional Information
  • Say Song Goh
  • Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
  • MR Author ID: 331333
  • Email: matgohss@nus.edu.sg
  • Tim N. T. Goodman
  • Affiliation: Department of Mathematics, The University of Dundee, Dundee DD1 4HN, Scotland, United Kingdom
  • Email: tgoodman@maths.dundee.ac.uk
  • S. L. Lee
  • Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
  • Email: matleesl@nus.edu.sg
  • Received by editor(s): September 26, 2006
  • Received by editor(s) in revised form: March 15, 2008
  • Published electronically: January 21, 2009
  • Additional Notes: This research was partially supported by the Wavelets and Information Processing Programme of the Centre for Wavelets, Approximation and Information Processing, National University of Singapore, under a grant from DSTA
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 78 (2009), 1537-1551
  • MSC (2000): Primary 65D07, 41A15; Secondary 42C40, 42C30
  • DOI: https://doi.org/10.1090/S0025-5718-09-02192-9
  • MathSciNet review: 2501062