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AB-Algorithm and its modifications for the spectral problems of linear pencils of matrices

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This paper describes and algorithm and its modifications for solving spectral problems for linear pencils of matrices both regular as well as singular.

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References

  1. Kublanovskaya, V.N.: TheAB-algorithm and its properties. LOMI, Leningrad Dept., Steklov Mathematical Institute, USSR Academy of Science, Leningrad,102, 42–60 (1980) (in Russian)

    Google Scholar 

  2. Faddeev, D.K., Kublanovskaya, V.N., Faddeeva, V.N.: Linear algebraic system with rectangular matrices. Modern Comput. Meth. I, p. 16–75, Kiev 1966, M. 1968 (in Russian)

    Google Scholar 

  3. Golub, G.H., Reinsch, C.: Singular value decomposition and least squares solutions, Numer. Math.14, (5), 403–420 (1970)

    Google Scholar 

  4. Kublanovskaya, V.N.: On spectral problems for polynomial pencils of matrices. LOMI, Leningrad Dept., Steklov Mathematical Institute, USSR Academy of Science, Leningrad,80, 83–87 (1978) (in Russian)

    Google Scholar 

  5. Kublanovskaya, V.N.: Newton's method for the computation of eigenvalues and eigenvectors of matrices. J. Comput. Math. Phys.12, (6), 1371–1380 (1972) (in Russian)

    Google Scholar 

  6. Konjkova, T.J.: Solution of the eigenvalue problem for the regular pencilD(λ)=λA 0−A by using deflating subspace, LOMI, Leningrad Dept., Steklov Mathematical Institute USSR Academy of Science, Leningrad,80, 48–65 (1978) (in Russian)

    Google Scholar 

  7. Faddeev, D.K., Faddeeva, V.N.: Computational methods in linear algebra, (translation) San Francisco Publishing, 1963

  8. Kublanovskaya, V.N.: On analysis of singular pencils of matrices, LOMI, Leningrad Dept., Steklov Mathematical Institute, USSR Academy of Science, Leningrad,70, 89–102 (1977) (in Russian)

    Google Scholar 

  9. Kublanovskaya, V.N., Simonova, V.N.: On certain modifications of theAB-algorithm. LOMI, Leningrad Dept., Stekov Mathematical Institute, USSR Academy of Science, Leningrad,111, 117–136 (1981) (in Russian)

    Google Scholar 

  10. Kublanovskaya, V.N.: On spectral problem for polynomial pencils of matrices. 2, LOMI, Leningrad Dept., Steklov Mathematical Institute, USSR Academy of Science, Leningrad,111, 109–116 (1981) (in Russian)

    Google Scholar 

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  1. Leningrad Department, USSR Academy of Science, Steklov Mathematical Institute, Leningrad, USSR

    V. N. Kublanovskaya

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  1. V. N. Kublanovskaya
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Kublanovskaya, V.N. AB-Algorithm and its modifications for the spectral problems of linear pencils of matrices. Numer. Math. 43, 329–342 (1984). https://doi.org/10.1007/BF01390177

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  • DOI: https://doi.org/10.1007/BF01390177

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