Constructing Finite Frames with a Given Spectrum

  • Matthew FickusEmail author
  • Dustin G. Mixon
  • Miriam J. Poteet
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


Broadly speaking, frame theory is the study of how to produce well-conditioned frame operators, often subject to nonlinear application-motivated restrictions on the frame vectors themselves. In this chapter, we focus on one particularly well-studied type of restriction: having frame vectors of prescribed lengths. We discuss two methods for iteratively constructing such frames. The first method, called Spectral Tetris, produces special examples of such frames, and only works in certain cases. The second method combines the idea behind Spectral Tetris with the classical theory of majorization; this method can build any such frame in terms of a sequence of interlacing spectra, called eigensteps.


Tight frames Schur-Horn Majorization Interlacing 



This work was supported by NSF DMS 1042701, NSF CCF 1017278, AFOSR F1ATA01103J001, AFOSR F1ATA00183G003, and the A.B. Krongard Fellowship. The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, the U.S. Government, or Thomas Jefferson.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Matthew Fickus
    • 1
    Email author
  • Dustin G. Mixon
    • 2
  • Miriam J. Poteet
    • 1
  1. 1.Department of MathematicsAir Force Institute of TechnologyWright-Patterson AFBUSA
  2. 2.Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA

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