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The LU-factorization of totally positive matrices. (English) Zbl 0274.15004


MSC:

15A15 Determinants, permanents, traces, other special matrix functions
15B48 Positive matrices and their generalizations; cones of matrices
15A24 Matrix equations and identities

References:

[1] Cryer, C. W., The LU-Factorization of Totally Positive Matrices, Technical Report No. 131 (December 1971), Computer Sciences Department, University of Wisconsin: Computer Sciences Department, University of Wisconsin Madison, Wisconsin
[2] Fox, L., An Introduction to Numerical Linear Algebra (1965), Oxford University Press: Oxford University Press New York · Zbl 0122.35701
[3] Gantmacher, F. R., The Theory of Matrices, Vol. 1 (1959), Chelsea, New York · Zbl 0085.01001
[4] Gantmacher, F. R.; Krein, M. G., Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme (1960), Akademie: Akademie Berlin · Zbl 0088.25103
[5] Henrici, P., Discrete Variable Methods in Ordinary Differential Equations (1962), Wiley: Wiley New York · Zbl 0112.34901
[6] Karlin, S., Total Positivity (1968), Stanford University Press: Stanford University Press Stanford · Zbl 0219.47030
[7] Koteljanskii, D. M., The theory of nonnegative and oscillating matrices, American Mathematical Society Translations, Vol. 27 (1963), American Mathematical Society: American Mathematical Society Providence, Series 2 · Zbl 0128.01802
[8] Marcus, M.; Hinc, H., A Survey of Matrix Theory and Inequalities (1964), Allyn and Bacon: Allyn and Bacon Boston · Zbl 0126.02404
[9] Markham, T. L., Factorizations of completely positive matrices, Proc. Camb. Phil. Soc., 69, 53-58 (1971) · Zbl 0205.33004
[10] Markham, T. L., Factorizations of nonnegative matrices, Proc. Amer. Math. Soc., 32, 45-47 (1972) · Zbl 0246.15022
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