Schwarz-like methods for approximate solving cooperative systems

Ivo Marek

Kybernetika (2004)

  • Volume: 40, Issue: 5, page [611]-624
  • ISSN: 0023-5954

Abstract

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The aim of this contribution is to propose and analyze some computational means to approximate solving mathematical problems appearing in some recent studies devoted to biological and chemical networks.

How to cite

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Marek, Ivo. "Schwarz-like methods for approximate solving cooperative systems." Kybernetika 40.5 (2004): [611]-624. <http://eudml.org/doc/33723>.

@article{Marek2004,
abstract = {The aim of this contribution is to propose and analyze some computational means to approximate solving mathematical problems appearing in some recent studies devoted to biological and chemical networks.},
author = {Marek, Ivo},
journal = {Kybernetika},
keywords = {Schwarz iterative solution; cooperative systems; steady states of evolution problems; Schwarz iterative solution; cooperative system; steady states of evolution problem},
language = {eng},
number = {5},
pages = {[611]-624},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Schwarz-like methods for approximate solving cooperative systems},
url = {http://eudml.org/doc/33723},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Marek, Ivo
TI - Schwarz-like methods for approximate solving cooperative systems
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 5
SP - [611]
EP - 624
AB - The aim of this contribution is to propose and analyze some computational means to approximate solving mathematical problems appearing in some recent studies devoted to biological and chemical networks.
LA - eng
KW - Schwarz iterative solution; cooperative systems; steady states of evolution problems; Schwarz iterative solution; cooperative system; steady states of evolution problem
UR - http://eudml.org/doc/33723
ER -

References

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  1. Benzi M., Frommer A., Nabben, R., Szyld D., 10.1007/s002110100275, Numer. Math. 89 (2002), 605–639 Zbl0991.65037MR1865505DOI10.1007/s002110100275
  2. Benzi M., Szyld D. B., 10.1007/s002110050265, Numer. Math. 76 (1997), 309–321 (1997) MR1452511DOI10.1007/s002110050265
  3. Berman A., Plemmons R., Non-negative Matrices in the Mathematical Sciences, Academic Press, New York 1979 MR0544666
  4. Bohl E., 10.1002/zamm.19910710707, Z. Angew. Math. Mech. 7/8 (1991), 223–231 (1991) Zbl0792.65057MR1121486DOI10.1002/zamm.19910710707
  5. Bohl E., Constructing amplification via chemical circuits, In: Biomedical Modeling Simulation (J. Eisarfeld, D. S. Leonis, and M. Witken, eds.), Elsevier Science Publ. B. V. 1992, pp. 331–334 (1992) 
  6. Bohl E., Structural amplification in chemical networks, In: Complexity, Chaos and Biological Evolution (E. Mosekilde and L. Mosekilde, eds.), Plenum Press, New York 1991, pp. 119–128 (1991) 
  7. Bohl E., Boos W., 10.1006/jtbi.1996.0342, J. Theoret. Biol. 186 (1997), 65–74 (1997) DOI10.1006/jtbi.1996.0342
  8. Bohl E., Lancaster P., 10.1016/0024-3795(93)90524-R, Linear Algebra Appl. 180 (1993), 65–74 (1993) MR1206409DOI10.1016/0024-3795(93)90524-R
  9. Bohl E., Marek I., 10.1016/0377-0427(95)00052-6, J. Comput. Appl. Math. 63 (1995), 27–47 (1995) Zbl0845.92003MR1365549DOI10.1016/0377-0427(95)00052-6
  10. Bohl E., Marek I., 10.1016/0377-0427(94)00081-B, An amplification effect measured in the cascade of vision. J. Comput. Appl. Math. 60 (1994), 13–28 (1994) MR1354645DOI10.1016/0377-0427(94)00081-B
  11. Bohl E., Marek I., 10.1007/BF01300579, Integral Equations Operator Theory 34 (1999), 251–269 (1999) MR1689389DOI10.1007/BF01300579
  12. Bohl E., Marek I., Existence and uniqueness results for nonlinear cooperative systems, Oper. Theory: Adv. Appl. 130 (2001), 153–170 Zbl1023.47052MR1902006
  13. Hille E., Phillips R. S., Functional Analysis and Semigroups (Amer, Math. Society Coll. Publ. Vol. XXXI). Third printing of Revised Edition Providence, RI 1968 
  14. Krein M. G., Rutman M. A., Linear operators leaving invariant a cone in a Banach space, Uspekhi Mat. Nauk III (1948), 1, 3–95. (In Russian.) English translation in Amer. Math. Soc. Transl. 26 (1950) (1948) Zbl0030.12902MR0027128
  15. Marek I., 10.1137/0119060, Comparison theorems and applications. SIAM J. Appl. Math. 19 (1970), 608–628 (1970) Zbl0219.47022MR0415405DOI10.1137/0119060
  16. Marek I., Szyld D., Algebraic Schwarz methods for the numerical solution of Markov chains, Linear Algebra Appl. Submitted Zbl1050.65030MR2066608
  17. Marek I., Žitný K., Analytic Theory of Matrices for Applied Sciences, Vol 1, (Teubner Texte zur Mathematik Band 60.) Teubner, Leipzig 1983 MR0731071
  18. Ortega J. M., Rheinboldt W., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York – San – Francisco – London 1970 Zbl0949.65053MR0273810
  19. Schaefer H. H., Banach Lattices and Positive Operators, Springer–Verlag, Berlin – Heidelberg – New York 1974 Zbl0296.47023MR0423039
  20. Stewart W. J., Introduction to the Numerical Solution of Markov Chains, Princeton University Press, Princeton, NJ 1994 Zbl0821.65099MR1312831
  21. Taylor A. E., Lay D. C., Introduction to Functional Analysis, Second edition. Wiley, New York 1980 Zbl0654.46002MR0564653
  22. Tralau C., Greller G., Pajatsch M., Boos, W., Bohl E., 10.1006/jtbi.2000.2140, J. Theoret. Biol. 207 (2000), 1–14 DOI10.1006/jtbi.2000.2140
  23. Varga R. S., Matrix Iterative Analysis, Prentice–Hall, Englewood Cliffs, NJ 1962. Second edition, revised and expanded. Springer–Verlag, Berlin – Heidelberg – New York 2000 (1962) MR1753713

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