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linear approximation

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linear approximation

In mathematics, the process of finding a straight line that closely fits a curve (function) at some location. Expressed as the linear equation y = ax + b, the values of a and b are chosen so that the line meets the curve at the chosen location, or value of x, and the slope of the line equals the rate of change of the curve (derivative of the function) at that location. For most curves, linear approximations are good only very close to the chosen x. Yet much of the theory of calculus, including the fundamental theorem of calculus and the mean-value theorem for derivatives, is based on such approximations.



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Our method behaves in a similar fashion, using a linear approximation to explore the search space globally and quickly; then it works to identify the moving object by frequently updating trust search regions," said Jiang.
In [2, 5-8], the authors introduced the optimal derivative, which is in fact a global approximation as opposed to the nonlinear perturbation of a linear equation, having a distinguished behavior with respect to the classical linear approximation in the neighborhood of the stationary point.
Deviations of the experimental limit strains from those obtained with linear approximation are not significant (Fig.
 
 
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