Abstract
We present a survey of recent results on the characterization of totally positive and strictly totally positive matrices. Included are some new characterizations which we have obtained in recent papers by using Neville elimination.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
T. Ando, Totally positive matrices. Linear Algebra Appl. 90:165–219 (1987).
A.S. Cavaretta; W. Dahmen; C.A. Micchelli and P.W. Smith, A factorization theorem for banded matrices. Linear Algebra Appl. 39:229–245 (1981).
C. Cryer, LU-factorization of totally positive matrices. Linear Algebra Appi. 7:83–92 (1973).
C. Cryer, Some properties of totally positive matrices. Linear Algebra Appl. 15:1–25 (1976).
C. de Boor and A. Pinkus, The approximation of a totally positive band matrix by a strictly totally positive one. Linear Algebra Appl. 43: 81–98 (1982).
M. Fekete, Über ein Problem von Laguerre, Rend. Conti Palermo 34: 89–100 (1913).
F.R. Gantmacher and M.G. Krein, Sur les matrices completement nonnegatives et oscillatoires, Compositio Math. 445–4276 (1937).
F.R. Gantmacher and M.G. Krein, Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme. Akademie-Verlag, Berlin (1960)
M. Gasca and G. Mühlbach, Generalized Schur complements and a test for total positivity, AppL Numer. Math. 3: 215–232 (1987).
M. Gasca and J.M. Peña, Total positivity and Neville elimination, to appear in Linear Algebra Appl. (1991).
M. Gasca and J.M. Pefia, Total positivity, QR factorization and Neville elimination. Preprint Univ. Zaragoza (1991).
M. Gasca and J.M. Peña, A matricial description of Neville elimination with applications to total positivity. Preprint Univ. Zaragoza (1991).
S. Karlin, Total Positivity. Stanford U.P., Stanford, California (1968).
K. Metelmann, Ein Kriterium für den Nachweis der Totalnichtnegativität von Bandmatrizen, Linear Algebra AppL 7: 163–171 (1973).
G. Mühlbach and M. Gasca, A test for strict total positivity via Neville elimination, in Current Trends in Matrix Theory (F. Uhlig and R. Groue, Eds.), Elsevier Science, 1987 pp. 225–232.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Gasca, M., Peña, J.M. (1992). On the Characterization of Totally Positive Matrices. In: Singh, S.P. (eds) Approximation Theory, Spline Functions and Applications. NATO ASI Series, vol 356. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2634-2_23
Download citation
DOI: https://doi.org/10.1007/978-94-011-2634-2_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5164-4
Online ISBN: 978-94-011-2634-2
eBook Packages: Springer Book Archive