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  • Articles  (2)
  • 65G05  (1)
  • AMS(MOS): Primary 65F05  (1)
  • Convex hull  (1)
  • 2005-2009
  • 1990-1994  (2)
  • Mathematics  (2)
Collection
  • Articles  (2)
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Keywords
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  • 2005-2009
  • 1990-1994  (2)
Year
Topic
  • 1
    Electronic Resource
    Electronic Resource
    Numerical stability of a convex hull algorithm for simple polygons (1993)
    Springer
    Algorithmica 10 (1993), S. 457-472 
    Details
    ISSN: 1432-0541
    Keywords: Convex hull ; Simple polygon ; Floating-point arithmetic ; Robust implementation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A numerically stable and optimalO(n)-time implementation of an algorithm for finding the convex hull of a simple polygon is presented. Stability is understood in the sense of a backward error analysis. A concept of the condition number of simple polygons and its impact on the performance of the algorithm is discussed. It is shown that if the condition number does not exceed (1+O(ε))/(3ε), then, in floating-point arithmetic with the unit roundoffε, the algorithm produces the vertices of a convex hull for slightly perturbed input points. The relative perturbation does not exceed 3ε(1+O(ε)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01891832
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On a direct method for the solution of nearly uncoupled Markov chains (1991)
    Springer
    Numerische Mathematik 59 (1991), S. 1-11 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): Primary 65F05 ; 65G05 ; Secondary: 15A51
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This note is concerned with the accuracy of the solution of nearly uncoupled Markov chains by a direct method based on the LU decomposition. It is shown that plain Gaussian elimination may fail in the presence of rounding errors. A modification of Gaussian elimination with diagonal pivoting and correction of small pivots is proposed and analyzed. It is shown that the accuracy of the solution is affected by two condition numbers associated with aggregation and the coupling respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385767
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    Paper (German National Licenses)
    Fulltext
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