2004
DOI: 10.1016/j.jco.2004.01.004
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On the complexity of curve fitting algorithms

Abstract: We study a popular algorithm for fitting polynomial curves to scattered data based on the least squares with gradient weights. We show that sometimes this algorithm admits a substantial reduction of complexity, and, furthermore, find precise conditions under which this is possible. It turns out that this is, indeed, possible when one fits circles but not ellipses or hyperbolas.Comment: 8 pages, no figure

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Cited by 14 publications
(7 citation statements)
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“…The value of f (u 1 ) within each of the 62 × 8 segments can then be approximated more efficiently using separate linear polynomials f (u 1 ) = a × u 1 + b. The coefficients a and b for each segment were calculated using the orthogonal least squares fit method [37] to minimize the residual error. The number of segments depends on the desired accuracy and on the size of memory that is available to store the coefficients of polynomials.…”
Section: Awgn Generatormentioning
confidence: 99%
“…The value of f (u 1 ) within each of the 62 × 8 segments can then be approximated more efficiently using separate linear polynomials f (u 1 ) = a × u 1 + b. The coefficients a and b for each segment were calculated using the orthogonal least squares fit method [37] to minimize the residual error. The number of segments depends on the desired accuracy and on the size of memory that is available to store the coefficients of polynomials.…”
Section: Awgn Generatormentioning
confidence: 99%
“…In the literature, almost all of the existing algorithms need a lot of execution time, choose significant peaks by examining the area of the peak or are too complex (Cheng and Sun, 2000;Chernov et al, 2004). Other algorithms ignore a peak if it is not large enough and experimental results showed that these approaches need a pre-processing of the histogram to work well, because of their noise sensitivity.…”
Section: Detection Of the Number Of Pixels Classesmentioning
confidence: 99%
“…Because they displayed different dynamic curves and the shapes and curvatures were different, it is difficult to fit these data with a common function [36][37][38][39][40][41]. Figures 6 and 7 both consist of the values of the RC, which can characterize the drug effect after exposure to different concentrations of gentamicin.…”
Section: Use Of Net Rc For Estimating the Inhibitory Rate Of Gentamicmentioning
confidence: 99%