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  • 1
    Electronic Resource
    Electronic Resource
    Accurate singular values and differential qd algorithms (1994)
    Springer
    Numerische Mathematik 67 (1994), S. 191-229 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65F15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We have discovered a new implementation of the qd algorithm that has a far wider domain of stability than Rutishauser's version. Our algorithm was developed from an examination of the {Cholesky~LR} transformation and can be adapted to parallel computation in stark contrast to traditional qd. Our algorithm also yields useful a posteriori upper and lower bounds on the smallest singular value of a bidiagonal matrix. The zero-shift bidiagonal QR of Demmel and Kahan computes the smallest singular values to maximal relative accuracy and the others to maximal absolute accuracy with little or no degradation in efficiency when compared with the LINPACK code. Our algorithm obtains maximal relative accuracy for all the singular values and runs at least four times faster than the LINPACK code.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050024
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Decomposition of a symmetric matrix (1976)
    Springer
    Numerische Mathematik 27 (1976), S. 95-109 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary An algorithm is presented to compute a triangular factorization and the inertia of a symmetric matrix. The algorithm is stable even when the matrix is not positive definite and is as fast as Cholesky. Programs for solving associated systems of linear equations are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01399088
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Lanczos versus subspace iteration for solution of eigenvalue problems (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 859-871 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we consider solution of the eigen problem in structural analysis using a recent version of the Lanczos method and the subspace method. The two methods are applied to examples and we conclude that the Lanczos method has advantages which are too good to overlook.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190608
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Approximate solutions and eigenvalue bounds from Krylov subspaces (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 115-133 
    Details
    ISSN: 1070-5325
    Keywords: Krylov subspace ; Lanczos process ; symmetric matrix ; conjugate gradients ; minimum residual ; Lehmann intervals ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Approximations to the solution of a large sparse symmetric system of equations are considered. The conjugate gradient and minimum residual approximations are studied without reference to their computation. Several different bases for the associated Krylov subspace are used, including the usual Lanczos basis. The zeros of the iteration polynomial for the minimum residual approximation (harmonic Ritz values) are characterized in several ways and, in addition, attractive convergence properties are established. The connection of these harmonic Ritz values to Lehmann's optimal intervals for eigenvalues of the original matrix appears to be new.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680020205
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Implicit Cholesky algorithms for singular values and vectors of triangular matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 507-531 
    Details
    ISSN: 1070-5325
    Keywords: Cholesky decomposition ; singular values ; eigenvalues ; null spaces ; noise spaces ; URV and ULV factorizations ; QR algorithm ; LR algorithm ; Jacobi methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The implicit Cholesky algorithm has been developed by several authors during the last 10 years but under different names. We identify the algorithm with a special version of Rutishauser's LR algorithm. Intermediate quantities in the transformation furnish several attractive approximations to the smallest singular value.The paper extols the advantages of using shifts with the algorithm. The nonorthogonal transformations improve accuracy.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nla.1680020604
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    Paper (German National Licenses)
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  • 6
    Book
    Book
    ¬The¬ symmetric eigenvalue problem; 20 (1998)
    Philadelphia, PA :SIAM,
    Details
    Title: ¬The¬ symmetric eigenvalue problem; 20
    Author: Parlett, Beresford N.
    Publisher: Philadelphia, PA :SIAM,
    Year of publication: 1998
    Pages: 398 S.
    Series Statement: Classics in applied mathematics 20
    Type of Medium: Book
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    Zuse Institute Berlin get availability status
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