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
Loading next page...
 
/lp/springer_journal/pentadiagonal-oscillatory-matrices-with-two-spectrum-in-common-INAOmdXRam
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

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off