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  • Articles  (8)
  • CR: 5.14  (8)
  • 1980-1984  (8)
  • 1950-1954
  • 1935-1939
  • 1984  (8)
  • Mathematics  (8)
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  • Articles  (8)
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  • 1980-1984  (8)
  • 1950-1954
  • 1935-1939
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  • Mathematics  (8)
  • 1
    Electronic Resource
    Electronic Resource
    An alternative givens ordering (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 83-90 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F05 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new Givens ordering is shown, empirically and by an approximate theoretical analysis, to take appreciably fewer stages than the standard scheme. Sharper error bounds than Gentleman's ensue, and the scheme is better suited to parallel computation. Other schemes, less efficient but more easily analysed, are discussed. The effect of a possible limit in practice on the number of simultaneous computations is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389639
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  • 2
    Electronic Resource
    Electronic Resource
    An accelerated bisection method for the calculation of eigenvalues of a symmetric tridiagonal matrix (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 153-160 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS): 15A18 ; 15-04 ; 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a method for the determination of eigenvalues of a symmetric tridiagonal matrix which combines Givens' Sturm bisection [4, 5] with interpolation, to accelerate convergence in high precision cases. By using an appropriate root of the absolute value of the determinant to derive the interpolation weight, results are obtained which compare favorably with the Barth, Martin, Wilkinson algorithm [1].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389644
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  • 3
    Electronic Resource
    Electronic Resource
    AB-Algorithm and its modifications for the spectral problems of linear pencils of matrices (1984)
    Springer
    Numerische Mathematik 43 (1984), S. 329-342 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F15 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper describes and algorithm and its modifications for solving spectral problems for linear pencils of matrices both regular as well as singular.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390177
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  • 4
    Electronic Resource
    Electronic Resource
    Applications of shortest path algorithms to matrix scalings (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 111-126 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F35 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A symmetric scaling of a nonnegative, square matrixA is a matrixXAX −1, whereX is a nonsingular, nonnegative diagonal matrix. By associating a family of weighted directed graphs with the matrixA we are able to adapt the shortest path algorithms to compute an optimal scaling ofA, where we call a symmetric scalingA′ ofA optimal if it minimizes the maximum of the ratio of non-zero elements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389759
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  • 5
    Electronic Resource
    Electronic Resource
    Zur Kondition des linearen Ausgleichsproblems mit linearen Gleichungen als Nebenbedingungen (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 139-152 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F20 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary F.L. Bauer has treated in several papers [1, 3, 4] the condition related to the solution of linear equations and to the algebraic eigenvalue problem. We study the condition for the linear least squares problem with linear equality constraints (problem LSE). A perturbation theory of problem LSE is presented and three condition numbers are defined. Problem LSE includes the linear least squares problem (problem LS). There are examples with identical solution of problem LSE and of problem LS. Sometimes the condition of problem LSE is better and sometimes the condition of problem LS is better. Several numerical tests illustrate the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389762
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  • 6
    Electronic Resource
    Electronic Resource
    Eigenvector matrices of symmetric tridiagonals (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 103-110 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 6540 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A simple test is given for determining whether a given matrix is the eigenvector matrix of an (unknown) unreduced symmetric tridiagonal matrix. A list of known necessary conditions is also provided. A lower bound on the separation between eigenvalues of tridiagonals follows from our Theorem 3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389758
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  • 7
    Electronic Resource
    Electronic Resource
    On neighbouring matrices with quadratic elementary divisors (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 1-21 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F 15 ; 65F20 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper presents new results on matrices with quadratic elementary divisors neighbouring a given matrixA and relates them to those given by Kakan. It shows that all results of this kind may give severe overestimates of the distance to the nearest defective matrix and that matrices with elementary divisors of degrees higher than two are often at a much greater distance than those with quadratic divisors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389751
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  • 8
    Electronic Resource
    Electronic Resource
    Comparisons of regular splittings of matrices (1984)
    Springer
    Numerische Mathematik 44 (1984), S. 23-35 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this article, new comparison theorems for regular splittings of matrices are derived. In so doing, the initial results of Varga in 1960 on regular splittings of matrices, and the subsequent unpublished results of Woźnicki in 1973 on regular splittings of matrices, will be seen to be special cases of these new comparison theorems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01389752
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