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  • Articles  (3)
  • Other Sources
  • CR: 5.14  (3)
  • 2015-2019
  • 1980-1984  (3)
  • Mathematics  (3)
  • Geography
  • Technology
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  • Articles  (3)
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  • Mathematics  (3)
  • Geography
  • Technology
  • 1
    Electronic Resource
    Electronic Resource
    Exact solution of linear equations usingP-adic expansions (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 137-141 
    Details
    ISSN: 0945-3245
    Keywords: (MR 1980) AMS(MOS) ; 65F05, 15A06, 10M10, 10A30 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A method is described for computing the exact rational solution to a regular systemAx=b of linear equations with integer coefficients. The method involves: (i) computing the inverse (modp) ofA for some primep; (ii) using successive refinements to compute an integer vector $$\bar x$$ such that $$A\bar x \equiv b$$ (modp m ) for a suitably large integerm; and (iii) deducing the rational solutionx from thep-adic approximation $$\bar x$$ . For matricesA andb with entries of bounded size and dimensionsn×n andn×1, this method can be implemented in timeO(n 3(logn)2) which is better than methods previously used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01459082
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  • 2
    Electronic Resource
    Electronic Resource
    A modified bisection algorithm for the determination of the eigenvalues of a symmetric tridiagonal matrix (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 417-419 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65F10 ; CR: 5.14
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A modification to the well known bisection algorithm [1] when used to determine the eigenvalues of a real symmetric matrix is presented. In the new strategy the terms in the Sturm sequence are computed only as long as relevant information on the required eigenvalues is obtained. The resulting algorithm usingincomplete Sturm sequences can be shown to minimise the computational work required especially when only a few eigenvalues are required. The technique is also applicable to other computational methods which use the bisection process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396441
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  • 3
    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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