least squares method

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.

Chebyshev approximation of multivariable functions with the interpolation

A method of constructing a Chebyshev approximation of multivariable functions by a generalized polynomial with the exact reproduction of its values at a given points is proposed.  It is based on the sequential construction of mean-power approximations, taking into account the interpolation condition.  The mean-power approximation is calculated using an iterative scheme based on the method of least squares with the variable weight function.  An algorithm for calculating the Chebyshev approximation parameters with the interpolation condition for absolute and relative error is described.  The

Optimization of least squares method to determine the harmonic coefficients on the sphere

Knowledge of the gravity field takes significance place in today's world. Such information is very important for performing of a number of contemporary problems related to satellite technologies. Such problems include: the launch of launch vehicles, satellites orbit prediction, the study of the surface of the oceans, transformation of normal and geodetic heights and more.