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  • 1975-1979  (3)
  • 1
    Electronic Resource
    Electronic Resource
    The convergence of the method of conjugate gradients at isolated extreme points of the spectrum (1975)
    Springer
    Numerische Mathematik 24 (1975), S. 85-93 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetA be a positive definite matrix with a simple eigenvalue λ1 that lies outside an interval [α, β] containing the remaining eigenvalues. Let the method of conjugate gradients be applied to the solution of the linear systemAz=b producing a sequence of iteratesz 0,z 1,... and an associated sequence of error vectorse i=z−z i. In this paper bounds are obtained for the component of the error vector lying along the eigenvector associated with λ1. The bounds imply that, provided λ1 is well separated from [α, β], this component will decrease rapidly, even when the matrixA is moderately ill conditioned.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01400959
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    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    The economical storage of plane rotations (1976)
    Springer
    Numerische Mathematik 25 (1976), S. 137-138 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Plane rotations, which have long been used in matrix computations to annihilate selected elements of a matrix, have the drawback that their definition requires two numbers. In this note it is shown how this information may be stably compacted into a single number.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01462266
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices (1976)
    Springer
    Numerische Mathematik 25 (1976), S. 123-136 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper describes a simultaneous iteration technique for computing a nested sequence of orthonormal bases for the dominant invariant subspaces of a non-Hermitian matrix. The method is particularly suited to large sparse eigenvalue problems, since it requires only that one be able to form the product of the matrix in question with a vector. A convergence theory for the method is developed and practical details are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01462265
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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