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Schwarz-Like Methods for Approximate Solving Cooperative Systems

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Large-Scale Scientific Computing (LSSC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2907))

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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.

Research has been supported by grant No.201/02/0595 of the Grant Agency of the Czech Republic and grant No. MSM 210000010 of the Ministry of Education of the Czech Republic.

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References

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

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Berman, A., Plemmons, R.: Non-negative Matrices in the Mathematical Sciences. Academic Press, London (1979)

    Google Scholar 

  4. Bohl, E., Boos, W.: Quantitative analysis of binding protein-mediated ABC transport system. J. Theor. Biology 186, 65–74 (1997)

    Article  Google Scholar 

  5. Bohl, E., Marek, I.: A model of amplification. J. Comput. Appl. Math. 63, 27–47 (1995)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Bohl, E., Marek, I.: Existence and uniqueness results for nonlinear cooperative systems. Operator Theory: Advances and Applications 130, 153–170 (2001)

    MathSciNet  Google Scholar 

  9. Hille, E., Phillips, R.S.: Functional Analysis and Semigroups, Rhode Island. Third printing of Revised Edition Providence, vol. XXXI. Amer. Math. Socitey Coll. Publ., Providence (1968)

    Google Scholar 

  10. Marek, I.: Frobenius theory of positive operators. Comparison theorems and applications. SIAM Journal on Applied Mathematics 19, 608–628 (1970)

    Article  MathSciNet  Google Scholar 

  11. Marek, I., Szyld, D.: Algebraic Schwarz methods for the numerical solution of Markov chains. Linear Algebra Appl (2003) (submitted)

    Google Scholar 

  12. Marek, I., Žitný, K.: Analytic Theory of Matrices for Applied Sciences. In: Teubner Texte zur Mathematik Band 60, Leipzig, vol. 1 (1983)

    Google Scholar 

  13. Ortega, J.M., Rheinboldt, W.: Iterative Solution of Nonlinear Equations In Several Variables. Academic Press, New York (1970)

    MATH  Google Scholar 

  14. Schaefer, H.H.: Banach Lattices and Positive Operators. Springer, Heidelberg (1974)

    MATH  Google Scholar 

  15. Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)

    MATH  Google Scholar 

  16. Taylor, A.E., Lay, D.C.: Introduction to Functional Analysis, 2nd edn. J. Wiley Publ., New York (1980)

    MATH  Google Scholar 

  17. 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. Theor. Biol. 207, 1–14 (2000)

    Article  Google Scholar 

  18. Varga, R.S.: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs (1962); 2nd edn. revised and expanded. Springer, Heidelberg (2000)

    Google Scholar 

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Marek, I. (2004). Schwarz-Like Methods for Approximate Solving Cooperative Systems. In: Lirkov, I., Margenov, S., Waśniewski, J., Yalamov, P. (eds) Large-Scale Scientific Computing. LSSC 2003. Lecture Notes in Computer Science, vol 2907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24588-9_3

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  • DOI: https://doi.org/10.1007/978-3-540-24588-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21090-0

  • Online ISBN: 978-3-540-24588-9

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