Geodesic
Effective solution of the problem of the optimal stability polynomial
Sbornik. Mathematics, Tome 196 (2005) no. 7, pp. 959-981 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An effective method for finding the polynomial approximating the exponential function with order 3 at the origin and deviating from 0 by at most 1 on the longest interval of the real axis is put forward. This problem is reduced to the solution of four equations on a 4-dimensional moduli space of algebraic curves. A numerical realization of this method using summation of linear Poincaré series is described. 
@article{SM_2005_196_7_a1,
     author = {A. B. Bogatyrev},
     title = {Effective solution of the problem of the optimal stability polynomial},
     journal = {Sbornik. Mathematics},
     pages = {959--981},
     year = {2005},
     volume = {196},
     number = {7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_7_a1/}
}
TY  - JOUR
AU  - A. B. Bogatyrev
TI  - Effective solution of the problem of the optimal stability polynomial
JO  - Sbornik. Mathematics
PY  - 2005
SP  - 959
EP  - 981
VL  - 196
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/SM_2005_196_7_a1/
LA  - en
ID  - SM_2005_196_7_a1
ER  - 
%0 Journal Article
%A A. B. Bogatyrev
%T Effective solution of the problem of the optimal stability polynomial
%J Sbornik. Mathematics
%D 2005
%P 959-981
%V 196
%N 7
%U http://geodesic.mathdoc.fr/item/SM_2005_196_7_a1/
%G en
%F SM_2005_196_7_a1
A. B. Bogatyrev. Effective solution of the problem of the optimal stability polynomial. Sbornik. Mathematics, Tome 196 (2005) no. 7, pp. 959-981. http://geodesic.mathdoc.fr/item/SM_2005_196_7_a1/

[1] Shtetter Kh., Analiz metodov diskretizatsii dlya obyknovennykh differentsialnykh uravnenii, Mir, M, 1978 | MR

[2] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii: zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999

[3] Franklin J. N., “Numerical stability in digital and analog computation for diffusion problems”, J. Math. Phys., 37:4 (1959), 305–315 | MR | Zbl

[4] Lebedev V. I., “Zoloterev polynomials and extremum problems”, Russian J. Numer. Anal. Math. Modelling, 9:3 (1994), 231–263 | MR | Zbl

[5] Riha W., “Optimal stability polynomials”, Computing, 9 (1972), 37–43 | DOI | MR | Zbl

[6] Lebedev V. I., “A new method for determining the roots of polynomials of least deviation on a segment with weight and subject to additional conditions. I, II”, Russian J. Numer. Anal. Math. Modelling, 8:3 (1993), 195–222 | MR | Zbl

[7] Abdulle A., “On roots and error constansts of optimal stability polynomials”, BIT, 40:1 (2000), 177–182 | DOI | MR | Zbl

[8] Verwer J. W., “Explicit Runge–Kutta methods for parabolic partial differential equations”, Appl. Numer. Math., 22:1–3 (1996), 359–379 | DOI | MR | Zbl

[9] Bogatyrëv A. B., “Effektivnyi podkhod k zadacham o naimenshem uklonenii”, Matem. sb., 193:12 (2002), 21–40 | MR | Zbl

[10] Bogatyrëv A. B., “Predstavlenie prostranstv modulei krivykh i vychislenie ekstremalnykh mnogochlenov”, Matem. sb., 194:4 (2003), 3–28 | MR | Zbl

[11] Bogatyrëv A. B., “Kombinatornoe opisanie prostranstva modulei krivykh i ekstremalnykh mnogochlenov”, Matem. sb., 194:10 (2003), 27–48 | MR

[12] Bernshtein S. N., Ekstremalnye svoistva mnogochlenov, ONTI, M.–L., 1937

[13] Griffits F., Kharris Dzh., Printsipy algebraicheskoi geometrii, Mir, M., 1982 | MR

[14] Krushkal S. L., Apanasov B. N., Gusevskii N. A., Kleinovy gruppy i uniformizatsiya v primerakh i zadachakh, SO Nauka, Novosibirsk, 1981

[15] Kurant R., Geometricheskaya teoriya funktsii, Nauka, M., 1968 | MR

[16] Schottky F., “Über eine specielle Function welche bei einer bestimmten linearen Transformation Ihres Argumenten unverändert bleibt”, J. Reine Angew. Math., 101 (1887), 227–272

[17] Burnside W., “On a class of authomorphic functions”, Proc. London Math. Soc. (3), 23 (1892), 49–88 | DOI

[18] Bogatyrëv A. B., “Ob effektivnom vychislenii mnogochlenov Chebyshëva dlya mnogikh otrezkov”, Matem. sb., 190:11 (1999), 15–50 | MR | Zbl

[19] Hejhal D. A., “Sur les parameters accessoires pour l'uniformization de Schottky”, C. R. Acad. Sci. Paris Sér. I Math., 279 (1974), 713–716 | MR | Zbl