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Advances in Computational Mathematics

, Volume 24, Issue 1–4, pp 297–309 | Cite as

Generation of finite tight frames by Householder transformations

  • De-Jun FengEmail author
  • Long Wang
  • Yang Wang
Article

Abstract

Finite tight frames are widely used for many applications. An important problem is to construct finite frames with prescribed norm for each vector in the tight frame. In this paper we provide a fast and simple algorithm for such a purpose. Our algorithm employs the Householder transformations. For a finite tight frame consisting of m vectors in ℝn or ℂn only O(nm) operations are needed. In addition, we also study the following question: Given a set of vectors in ℝn or ℂn, how many additional vectors, possibly with constraints, does one need to add in order to obtain a tight frame?

Keywords

frames tight frame tight frame matrix Householder matrix condition number 

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingP.R. China
  2. 2.Mathematics DepartmentSouthern Polytechnic State UniversityMariietaU.S.A.
  3. 3.School of MathematicsGeorgia Institute of TechnologyAtlantaU.S.A.

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