Schwarz-like methods for approximate solving cooperative systems
Kybernetika, Tome 40 (2004) no. 5, pp. 611-624 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 47B60, 65F10, 65M55
Keywords: Schwarz iterative solution; cooperative systems; steady states of evolution problems
@article{KYB_2004_40_5_a6,
     author = {Marek, Ivo},
     title = {Schwarz-like methods for approximate solving cooperative systems},
     journal = {Kybernetika},
     pages = {611--624},
     year = {2004},
     volume = {40},
     number = {5},
     mrnumber = {2121000},
     zbl = {1249.65070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2004_40_5_a6/}
}
TY  - JOUR
AU  - Marek, Ivo
TI  - Schwarz-like methods for approximate solving cooperative systems
JO  - Kybernetika
PY  - 2004
SP  - 611
EP  - 624
VL  - 40
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/KYB_2004_40_5_a6/
LA  - en
ID  - KYB_2004_40_5_a6
ER  - 
%0 Journal Article
%A Marek, Ivo
%T Schwarz-like methods for approximate solving cooperative systems
%J Kybernetika
%D 2004
%P 611-624
%V 40
%N 5
%U http://geodesic.mathdoc.fr/item/KYB_2004_40_5_a6/
%G en
%F KYB_2004_40_5_a6
Marek, Ivo. Schwarz-like methods for approximate solving cooperative systems. Kybernetika, Tome 40 (2004) no. 5, pp. 611-624. http://geodesic.mathdoc.fr/item/KYB_2004_40_5_a6/

[1] Benzi M., Frommer A., Nabben, R., Szyld D.: Algebraic theory of multiplicative Schwarz methods. Numer. Math. 89 (2002), 605–639 | DOI | MR | Zbl

[2] Benzi M., Szyld D. B.: Existence and uniqueness of splittings for stationary iterative methods with applications to alterning methods. Numer. Math. 76 (1997), 309–321 | DOI | MR

[3] Berman A., Plemmons R.: Non-negative Matrices in the Mathematical Sciences. Academic Press, New York 1979 | MR

[4] Bohl E.: A boundary layer phenomenon for linear systems with a rank deficient matrix. Z. Angew. Math. Mech. 7/8 (1991), 223–231 | DOI | MR | Zbl

[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

[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

[7] Bohl E., Boos W.: Quantitative analysis of binding protein-mediated ABC transport system. J. Theoret. Biol. 186 (1997), 65–74 | DOI

[8] Bohl E., Lancaster P.: Perturbation of spectral inverses applied to a boundary layer phenomenon arizing in chemical networks. Linear Algebra Appl. 180 (1993), 65–74 | DOI | MR

[9] Bohl E., Marek I.: A model of amplification. J. Comput. Appl. Math. 63 (1995), 27–47 | DOI | MR | Zbl

[10] Bohl E., Marek I.: A nonlinear model involving M-operators. An amplification effect measured in the cascade of vision. J. Comput. Appl. Math. 60 (1994), 13–28 | DOI | MR

[11] Bohl E., Marek I.: A stability theorem for a class of linear evolution problems. Integral Equations Operator Theory 34 (1999), 251–269 | DOI | MR

[12] Bohl E., Marek I.: Existence and uniqueness results for nonlinear cooperative systems. Oper. Theory: Adv. Appl. 130 (2001), 153–170 | MR | Zbl

[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) | MR | Zbl

[15] Marek I.: Frobenius theory of positive operators. Comparison theorems and applications. SIAM J. Appl. Math. 19 (1970), 608–628 | DOI | MR | Zbl

[16] Marek I., Szyld D.: Algebraic Schwarz methods for the numerical solution of Markov chains. Linear Algebra Appl. Submitted | MR | Zbl

[17] Marek I., Žitný K.: Analytic Theory of Matrices for Applied Sciences, Vol 1. (Teubner Texte zur Mathematik Band 60.) Teubner, Leipzig 1983 | MR

[18] Ortega J. M., Rheinboldt W.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York – San – Francisco – London 1970 | MR | Zbl

[19] Schaefer H. H.: Banach Lattices and Positive Operators. Springer–Verlag, Berlin – Heidelberg – New York 1974 | MR | Zbl

[20] Stewart W. J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton, NJ 1994 | MR | Zbl

[21] Taylor A. E., Lay D. C.: Introduction to Functional Analysis. Second edition. Wiley, New York 1980 | MR | Zbl

[22] Tralau C., Greller G., Pajatsch M., Boos, W., Bohl E.: Mathematical treatment of transport data of bacterial transport system to estimate limitation in diffusion through the outer membrane. J. Theoret. Biol. 207 (2000), 1–14 | DOI

[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 | MR