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  • Artikel  (11)
  • Artikel: DFG Deutsche Nationallizenzen  (11)
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  • Artikel: DFG Deutsche Nationallizenzen  (11)
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  • Springer  (11)
  • American Chemical Society (ACS)
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  • 2015-2019
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  • 1
    Digitale Medien
    Digitale Medien
    Fast Givens rotations for orthogonal similarity transformations (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 47-56 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65F30 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Fast Givens rotations with half as many multiplications are proposed for orthogonal similarity transformations and a matrix notation is introduced to describe them more easily. Applications are proposed and numerical results are examined for the Jacobi method, the reduction to Hessenberg form and the QR-algorithm for Hessenberg matrices. It can be seen that in general fast Givens rotations are competitive with Householder reflexions and offer distinct advantages for sparse matrices.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01459074
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Exact solution of linear equations usingP-adic expansions (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 137-141 
    Details
    ISSN: 0945-3245
    Schlagwort(e): (MR 1980) AMS(MOS) ; 65F05, 15A06, 10M10, 10A30 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01459082
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  • 3
    Digitale Medien
    Digitale Medien
    Error bounds for computed eigenvalues and eigenvectors. II (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 201-206 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F05, 65F15, 65H10 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper, motivated by Symm-Wilkinson's paper [5], we describe a method which finds the rigorous error bounds for a computed eigenvalue λ(0) and a computed eigenvectorx (0) of any matrix A. The assumption in a previous paper [6] that λ(0),x (0) andA are real is not necessary in this paper. In connection with this method, Symm-Wilkinson's procedure is discussed, too.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01400539
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  • 4
    Digitale Medien
    Digitale Medien
    LU decompositions of generalized diagonally dominant matrices (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 57-69 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F05 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Using the simple vehicle ofM-matrices, the existence and stability ofLU decompositions of matricesA which can be scaled to diagonally dominant (possibly singular) matrices are investigated. Bounds on the growth factor for Gaussian elimination onA are derived. Motivation for this study is provided in part by applications to solving homogeneous systems of linear equationsAx=0, arising in Markov queuing networks, input-output models in economics and compartmental systems, whereA or −A is an irreducible, singularM-matrix. This paper extends earlier work by Funderlic and Plemmons and by Varga and Cai.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01459075
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  • 5
    Digitale Medien
    Digitale Medien
    Computing theCS decomposition of a partitioned orthonormal matrix (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 297-306 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65F25 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper describes an algorithm for simultaneously diagonalizing by orthogonal transformations the blocks of a partitioned matrix having orthonormal columns.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396447
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  • 6
    Digitale Medien
    Digitale Medien
    On fixed point linear equations (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 53-59 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; 47B55 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary By means of successive partial substitutions it is possible to obtain new fixed point linear equations from old ones and it is interesting to determine how the spectral radius of the corresponding matrices varies. We prove that, when the original matrix is nonnegative, this variation is decreasing or increasing, depending on whether the original matrix has its spectral radius smaller or greater than 1. We answer in this way a question posed by F. Robert in [5].
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01395808
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  • 7
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): AMS(MOS): 65F10 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396441
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  • 8
    Digitale Medien
    Digitale Medien
    A contribution to the theory of condition (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 85-96 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS65F05 ; 65F 15 ; 65F 20 ; 65F 35 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary In this paper the use of the condition number of a problem, as defined by Rice in 1966, is discussed. For the eigenvalue, eigenvector, and linear least squares problems either condition numbers according to various norms are determined or lower and upper bounds for them are derived.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01399313
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  • 9
    Digitale Medien
    Digitale Medien
    Inversion of tridiagonal matrices (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 333-345 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 15 A 09, 15-04 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper presents a simple algorithm for inverting nonsymmetric tridiagonal matrices that leads immediately to closed forms when they exist. Ukita's theorem is extended to characterize the class of matrices that have tridiagonal inverses.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396436
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  • 10
    Digitale Medien
    Digitale Medien
    On the convergence of the symmetric SOR method for matrices with red-black ordering (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 113-117 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; CR: 5.14
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We prove that if the matrixA has the structure which results from the so-called “red-black” ordering and ifA is anH-matrix then the symmetric SOR method (called the SSOR method) is convergent for 0〈ω〈2. In the special case thatA is even anM-matrix we show that the symmetric single-step method cannot be accelerated by the SSOR method. Symmetry of the matrixA is not assumed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01399315
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