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  • 65F10  (1)
  • AMS(MOS) 65F10  (1)
  • Breast volume  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    A note on the SSOR and USSOR iterative methods applied top-cyclic matrices (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 109-121 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65F10 ; CR:G.1
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The purpose of this note is threefold:i) to derive the new functional equation, $$\begin{gathered} \left[ {\lambda - \left( {1 - \omega } \right)\left( {1 - \hat \omega } \right)} \right]^p = \lambda ^k \left[ {\lambda \omega + \hat \omega - \omega \hat \omega } \right]^{\left| {\zeta _L } \right| - k} \left[ {\lambda \hat \omega + \omega - \omega \hat \omega } \right]^{\left| {\zeta _U } \right| - k} \hfill \\ \cdot \left( {\omega + \hat \omega - \omega \hat \omega } \right)^{2k} \mu ^p , \hfill \\ \end{gathered} $$ which couples the nonzero eigenvalues of the USSOR iteration matrix $$T_{\omega ,\hat \omega } $$ with the eigenvalues μ of the associated block Jacobi matrixB in thep-cyclic case,ii) to interpret the exponentk in this equation by means of graph theory, andiii) to connect the above equation with known results in the literature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01409780
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  • 2
    Electronic Resource
    Electronic Resource
    A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations (1993)
    Springer
    Numerische Mathematik 64 (1993), S. 213-240 
    Details
    ISSN: 0945-3245
    Keywords: 65F10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present here a new hybrid method for the iterative solution of large sparse nonsymmetric systems of linear equations, say of the formAx=b, whereA ∈ ℝ N, N , withA nonsingular, andb ∈ ℝ N are given. This hybrid method begins with a limited number of steps of the Arnoldi method to obtain some information on the location of the spectrum ofA, and then switches to a Richardson iterative method based on Faber polynomials. For a polygonal domain, the Faber polynomials can be constructed recursively from the parameters in the Schwarz-Christoffel mapping function. In four specific numerical examples of non-normal matrices, we show that this hybrid algorithm converges quite well and is approximately as fast or faster than the hybrid GMRES or restarted versions of the GMRES algorithm. It is, however, sensitive (as other hybrid methods also are) to the amount of information on the spectrum ofA acquired during the first (Arnoldi) phase of this procedure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01388688
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  • 3
    Electronic Resource
    Electronic Resource
    Validity and reliability of biostereometric measurement of the human female breast (1986)
    Springer
    Annals of biomedical engineering 14 (1986), S. 1-14 
    Details
    ISSN: 1573-9686
    Keywords: Stereophotogrammetry ; Validity ; Reliability ; Breast volume
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A measurement technique has been developed for application in the area of noninvasive breast cancer detection. The measurement process involves the use of closerange stereophotogrammetry as a data acquisition device necessary for determination of breast volume and volume distribution. This report details the methodology used to acquire and analyze stereopair photographs necessary to document the validity and reliability of this application. The volume of a test object was determined by both water displacement and stereophotogrammetric analysis to estimate the precision of the proposed methodology. Additionally, the reliability component of the study was documented by analyzing variability of coordinates representing a series of locations marked on the surface of an irregularly shaped object. Both tests confirm that this stereometric analysis is a reliable and valid method of measurement and may be well suited for further development in the field of breast cancer detection.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02364645
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