Pentadiagonal Oscillatory Matrices with Two Spectrum in Common

Pentadiagonal Oscillatory Matrices with Two Spectrum in Common We denote the spectrum of an square matrix A by σ(A), and that of the matrix obtained by deleting the first i rows and columns of A by σ i (A). It is known that a symmetric pentadiagonal oscillatory (SPO) matrix may be constructed from σ, σ 1 and σ 2. The pairs σ, σ 1 and σ 1, σ 2 must interlace; the construction is not unique; and the conditions on the data which ensure that A is oscillatory are extremely complicated. Given one SPO matrix A, the paper shows that operations may be applied to A to construct a family of such matrices with σ and σ 1 in common. Moreover, given one totally positive (TP) matrix A, we construct a family of TP matrices with σ, σ 1 and σ 2 in common. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Pentadiagonal Oscillatory Matrices with Two Spectrum in Common

Positivity , Volume 10 (4) – Jul 11, 2006
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Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2006 by Birkhäuser Verlag, Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-005-5091-7
Publisher site
See Article on Publisher Site

Abstract

We denote the spectrum of an square matrix A by σ(A), and that of the matrix obtained by deleting the first i rows and columns of A by σ i (A). It is known that a symmetric pentadiagonal oscillatory (SPO) matrix may be constructed from σ, σ 1 and σ 2. The pairs σ, σ 1 and σ 1, σ 2 must interlace; the construction is not unique; and the conditions on the data which ensure that A is oscillatory are extremely complicated. Given one SPO matrix A, the paper shows that operations may be applied to A to construct a family of such matrices with σ and σ 1 in common. Moreover, given one totally positive (TP) matrix A, we construct a family of TP matrices with σ, σ 1 and σ 2 in common.

Journal

PositivitySpringer Journals

Published: Jul 11, 2006

References

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