| Title:
|
On stable polynomials (English) |
| Author:
|
Nekvinda, Miloslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1989 |
| Pages:
|
177-196 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hurwitz polynomials |
| Keyword:
|
expository paper |
| Keyword:
|
Hurwitz-Routh criterion |
| Keyword:
|
stable polynomial |
| Keyword:
|
Hermite |
| Keyword:
|
decompositon of Schur |
| MSC:
|
01A60 |
| MSC:
|
12D10 |
| MSC:
|
26C10 |
| MSC:
|
30C15 |
| MSC:
|
34D10 |
| MSC:
|
93D99 |
| idZBL:
|
Zbl 0703.12001 |
| idMR:
|
MR0996895 |
| DOI:
|
10.21136/AM.1989.104347 |
| . |
| Date available:
|
2008-05-20T18:36:34Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104347 |
| . |
| Reference:
|
[1] Ch. Hermite: Sur le nombre des racines d'une équation algébrique comprises entre des limites données.Crelles J. 52, 39 (1856). |
| Reference:
|
[2] J. Routh: A treatise on the stability of a given state of motion.London 1877. |
| Reference:
|
[3] A. Hurwitz: Über die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Teilen besitzt.Math. Ann. 46, 273 (1895). Zbl 0962.01500, MR 1510884, 10.1007/BF01446812 |
| Reference:
|
[4] J. Schur: Über die algebraischen Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen.Z. angew. Math. Mech, 1, 307 (1921). 10.1002/zamm.19210010405 |
| Reference:
|
[5] 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. Zbl 0068.05803, MR 0073686 |
| Reference:
|
[6] H. Cremer F. H. Effertz: Über die algebraischen Kriterien für die Stabilität von Regulungsystemen.Math. Ann. 137 (1959), 328-350. MR 0104684, 10.1007/BF01360969 |
| Reference:
|
[7] R. Bellman: Introduction to Matrix Analysis.Mc Graw-Нill Book Company, New York 1960. Zbl 0124.01001, MR 0122820 |
| Reference:
|
[8] F. R. Gantmacher: Theory of Matrices.(Russian) Izd. Nauka, Moskva 1966. MR 0202725 |
| Reference:
|
[9] B. P. Demidowich: Lectures on the Mathematical Theory of Stability.(Russian) Izd. Nauka, Moskva 1967. MR 0226126 |
| Reference:
|
[10] J. Hale: Theory of Functional Differential Equations.Springer-Verlag, New York 1977. Zbl 0352.34001, MR 0508721 |
| . |
