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Mat. Sb., 2005, Volume 196, Number 7, Pages 27–50 (Mi msb1375)  

This article is cited in 8 scientific papers (total in 8 papers)

Effective solution of the problem of the optimal stability polynomial

A. B. Bogatyrevab

a Moscow Institute of Physics and Technology
b Institute of Numerical Mathematics, Russian Academy of Sciences

Abstract: 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.

DOI: https://doi.org/10.4213/sm1375

Full text: PDF file (445 kB)
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English version:
Sbornik: Mathematics, 2005, 196:7, 959–981

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A29, 65L06; Secondary 32G15
Received: 19.03.2004 and 28.03.2005

Citation: A. B. Bogatyrev, “Effective solution of the problem of the optimal stability polynomial”, Mat. Sb., 196:7 (2005), 27–50; Sb. Math., 196:7 (2005), 959–981

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    Erratum

    This publication is cited in the following articles:
    1. Bogatyrev, A, “Effective computation of optimal stability polynomials”, Calcolo, 41:4 (2004), 247  crossref  mathscinet  zmath  isi  elib
    2. L. M. Skvortsov, “Prostoi sposob postroeniya mnogochlenov ustoichivosti dlya yavnykh stabilizirovannykh metodov Runge–Kutty”, Matem. modelirovanie, 23:1 (2011), 81–86  mathnet  mathscinet
    3. L. M. Skvortsov, “Explicit stabilized Runge–Kutta methods”, Comput. Math. Math. Phys., 51:7 (2011), 1153–1166  mathnet  crossref  mathscinet  isi  elib
    4. A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. David Ketcheson, Aron Ahmadia, “Optimal stability polynomials for numerical integration of initial value problems”, Commun. Appl. Math. Comput. Sci, 7:2 (2012), 247  crossref  mathscinet  isi
    6. Bogatyrev A.B. Goreinov S.A. Lyamaev S.Yu., “Eflcient Synthesis of Optimal Multiband Filter”, Russ. J. Numer. Anal. Math. Model, 32:4 (2017), 217–223  crossref  mathscinet  zmath  isi  scopus
    7. Ait-Haddou R., “New Stability Results For Explicit Runge-Kutta Methods”, Bit, 59:3 (2019), 585–612  crossref  mathscinet  zmath  isi
    8. Bogatyrev A., “Recent Progress in Optimization of Multiband Electrical Filters”, Approximation and Optimization: Algorithms, Complexity and Applications, Springer Optimization and Its Applications, 145, ed. Demetriou I. Pardalos P., Springer International Publishing Ag, 2019, 135–149  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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