# On stable polynomials

Aplikace matematiky (1989)

- Volume: 34, Issue: 3, page 177-196
- ISSN: 0862-7940

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topNekvinda, Miloslav. "On stable polynomials." Aplikace matematiky 34.3 (1989): 177-196. <http://eudml.org/doc/15575>.

@article{Nekvinda1989,

abstract = {The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.},

author = {Nekvinda, Miloslav},

journal = {Aplikace matematiky},

keywords = {Hurwitz polynomials; expository paper; Hurwitz-Routh criterion; stable polynomial; Hermite; decompositon of Schur; Hurwitz polynomials; expository paper; Hurwitz-Routh criterion},

language = {eng},

number = {3},

pages = {177-196},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On stable polynomials},

url = {http://eudml.org/doc/15575},

volume = {34},

year = {1989},

}

TY - JOUR

AU - Nekvinda, Miloslav

TI - On stable polynomials

JO - Aplikace matematiky

PY - 1989

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 34

IS - 3

SP - 177

EP - 196

AB - The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.

LA - eng

KW - Hurwitz polynomials; expository paper; Hurwitz-Routh criterion; stable polynomial; Hermite; decompositon of Schur; Hurwitz polynomials; expository paper; Hurwitz-Routh criterion

UR - http://eudml.org/doc/15575

ER -

## References

top- Ch. Hermite, Sur le nombre des racines d'une équation algébrique comprises entre des limites données, Crelles J. 52, 39 (1856).
- J. Routh, A treatise on the stability of a given state of motion, London 1877. Zbl17.0315.02
- A. Hurwitz, 10.1007/BF01446812, Math. Ann. 46, 273 (1895). Zbl0962.01500MR1510884DOI10.1007/BF01446812
- J. Schur, 10.1002/zamm.19210010405, Z. angew. Math. Mech, 1, 307 (1921). (1921) Zbl48.0082.03DOI10.1002/zamm.19210010405
- L. S. Pontryagin, On the zeros of some elementary transcendental functions, (Russian) Izv. Ak. Nauk SSSR, Ser. Mat. 6 (1942), 115-134. English Translation: Amer. Math. Soc. Transl. (2) 1 (1955), 95-110. (1942) Zbl0068.05803MR0073686
- H. Cremer F. H. Effertz, 10.1007/BF01360969, Math. Ann. 137 (1959), 328-350. (1959) Zbl0092.01604MR0104684DOI10.1007/BF01360969
- R. Bellman, Introduction to Matrix Analysis, Mc Graw-Нill Book Company, New York 1960. (1960) Zbl0124.01001MR0122820
- F. R. Gantmacher, Theory of Matrices, (Russian) Izd. Nauka, Moskva 1966. (1966) Zbl0136.00410MR0202725
- B. P. Demidowich, Lectures on the Mathematical Theory of Stability, (Russian) Izd. Nauka, Moskva 1967. (1967) MR0226126
- J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York 1977. (1977) Zbl0352.34001MR0508721

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