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  • Advanced Start  (1)
  • Curve Fitting  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    A dual method for discrete Chebychev curve fitting (1980)
    Springer
    Mathematical programming 19 (1980), S. 186-199 
    Details
    ISSN: 1436-4646
    Keywords: Regression ; Curve Fitting ; Min—Max ; Chebychev
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a special purpose dual algorithm for obtaining a Chebychev approximation to an overdetermined system of linear equations. The method is founded on the principles of linear programming and is designed to take advantage of the problem's special structure. It is shown that, while maintaining a reduced basis, certain iterations of the standard dual algorithm may be combined into one. Two computer code implementations of the method are discussed and a computational comparison with another algorithm for Chebychev approximation is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581640
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Least absolute value and chebychev estimation utilizing least squares results (1982)
    Springer
    Mathematical programming 24 (1982), S. 346-352 
    Details
    ISSN: 1436-4646
    Keywords: Least Absolute Values ; Chebychev Norm ; Regression ; Minimax ; Advanced Start ; Least Squares
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In exploratory data analysis and curve fitting in particular, it is often desirable to observe residual values obtained with different estimation criteria. The goal with most linear model curve-fitting procedures is to minimize, in some sense, the vector of residuals. Perhaps three of the most common estimation criteria require minimizing: the sum of the absolute residuals (least absolute value or L1 norm); the sum of the squared residuals (least squares or L2 norm); and the maximum residual (Chebychev or L∞ norm). This paper demonstrates that utilizing the least squares residuals to provide an advanced start for the least absolute value and Chebychev procedures results in a significant reduction in computational effort. Computational results are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585115
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    Paper (German National Licenses)
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