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Solution of the Cauchy problem. Methods and algorithms

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Abstract

The Cauchy problem for systems of algebraic-differential equations with constant coefficients, i.e., for systems of ordinary differential equations that cannot be resolved for the highest derivative, both regular of index γ>0 and singular of arbitrary index γ, is considered, Bibliography: 11 titles.

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References

  1. V. N. Kublanovskaya, “Rank division algorithms and their applications”,J. Numer. Lin. Algebra, Appl.,1, No. 2, 199–213 (1992).

    MathSciNet  Google Scholar 

  2. G. Golub and W. Kahan, “Calculating the singular values and pseudoinverse of a matrix”SIAM J. Numer. Anal., Ser. B2,2, No. 2, 205–224 (1965).

    Article  MathSciNet  Google Scholar 

  3. G. Golub and C. Reinsch. “Singular value decomposition and least squares solutions”,Numer. Math.,14, No. 5, 403–420 (1970).

    Article  MATH  MathSciNet  Google Scholar 

  4. D. K. Faddeev, V. N. Kublanovskaya, and V. N. Faddeeva, “Linear algebraic systems with rectangular matrices”, In:Modern Numerical Methods [in Russian], Vol. 1. Moscow (1969), pp. 16–75.

  5. V. A. Belyi, V. B. Khazanov, and V. N. Kublanovskaya, “Spectral problems for matrix pencils. III”,Sov. J. Numer. Anal. Math. Modelling,4, No. 1, 19–51 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  6. V. N. Kublanovskaya, “The AB-algorithm and its modifications for spectral problems of linear pencils of matrices”,Numer. Math.,43, 329–342 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. N. Kublanovskaya, “TheAB-algorithm and its properties”,Zap. Nauchn. Semin. LOMI,102, 42–66 (1980).

    MathSciNet  Google Scholar 

  8. V. N. Kublanovskaya and V. N. Simonova, “On some properties of theAB-algorithm”.Zap. Nauchn. Semin. LOMI,111, 117–137 (1981).

    MATH  MathSciNet  Google Scholar 

  9. C. B. Moller and G. M. Stewart, “An algorithm for generalized matrix eigenvalue problems”,SIAM J. Numer. Anal.,10, No. 2, 241–256 (1973).

    Article  MathSciNet  Google Scholar 

  10. T. Ya. Kon’kova, L. T. Savinova, V. N. Simonova, N. B. Cziborskaya, and T. V. VashenkoThe Package of Programs “Spectrum”, [in Russian], Nauka, Leningrad (1984).

    Google Scholar 

  11. T. Ya. Kon’kova and V. N. Simonova, “Library of the MATLAB functions for polynomial matrices”,Zap. Nauchn. Semin. POMI,219, 53–80 (1994).

    MATH  Google Scholar 

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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 70–123.

Translated by V. N. Kublanovskaya.

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Kublanovskaya, V.N. Solution of the Cauchy problem. Methods and algorithms. J Math Sci 101, 3267–3299 (2000). https://doi.org/10.1007/BF02672772

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