Skip to Main Content

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 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Algorithms for matrix extension and orthogonal wavelet filter banks over algebraic number fields
HTML articles powered by AMS MathViewer

by Bin Han and Xiaosheng Zhuang PDF
Math. Comp. 82 (2013), 459-490 Request permission


As a finite dimensional linear space over the rational number field $\mathbb {Q}$, an algebraic number field is of particular importance and interest in mathematics and engineering. Algorithms using algebraic number fields can be efficiently implemented involving only integer arithmetics. We observe that all known finitely supported orthogonal wavelet low-pass filters in the literature have coefficients coming from an algebraic number field. Therefore, it is of theoretical and practical interest for us to consider orthogonal wavelet filter banks over algebraic number fields. In this paper, we formulate the matrix extension problem over any general subfield of $\mathbb {C}$ (including an algebraic number field as a special case), and we provide step-by-step algorithms to implement our main results. As an application, we obtain a satisfactory algorithm for constructing orthogonal wavelet filter banks over algebraic number fields. Several examples are provided to illustrate the algorithms proposed in this paper.
Similar Articles
Additional Information
  • Bin Han
  • Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
  • MR Author ID: 610426
  • Email:
  • Xiaosheng Zhuang
  • Affiliation: Institut für Mathematik, Technische Universität, 10623 Berlin, Germany
  • Email:
  • Received by editor(s): April 9, 2011
  • Received by editor(s) in revised form: September 7, 2011
  • Published electronically: May 24, 2012
  • Additional Notes: This research was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC Canada) under Grant RGP 228051.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 82 (2013), 459-490
  • MSC (2010): Primary 42C40, 41A05; Secondary 42C15, 65T60
  • DOI:
  • MathSciNet review: 2983032