Rational Expression

Chebyshev approximation by the exponent from a rational expression

A method for constructing Chebyshev approximation with relative error of the exponential from a rational expression is proposed.  It implies constructing an intermediate Chebyshev approximation with absolute error by a rational expression of the logarithm of the function being approximated.  The approximation by a rational expression is calculated as the boundary mean-power approximation using an iterative scheme based on the least squares method with two variable weight functions.  The presented results of solving test examples confirm the fast convergence of the metho

MINIMAX APPROXIMATION OF THE RESISTANCE-TEMPERATURE THERMISTOR’S DEPENDENCE

The evidence to support feasibility of using minimax approximation to calculate the parameters of thermistors’ thermometric characteristic models has been provided. Minimax approximation ensures the achievement of the minimum possible calibration error, while the least squares method minimizes the sum of squared errors. A rational expression has been proposed to describe the dependence of temperature on thermistor’s resistance. The effectiveness of the model in the form of a rational expression is illustrated with actual calibration results.