Application of Chebyshev Approximation to Curve Fitting

Abstract

The standard methods of curve and surface fitting are based upon least squares approximation of given data. An alternative is the principle of uniform (Chebyshev) approximation. This approach can be advantageous and even essential in certain technical applications, such as the engineering problem described in section 2. The general problem of uniform curve fitting to given data with some generalizations and two special cases are discussed in section 3. It should be noted that these problems are different from those of standard Chebyshev approximation where a given function is approximated by an element of a linear or nonlinear class of functions. However, as will be shown in section 4, certain principles known from approximation theory such as optimality conditions and alternation properties can be retrieved here.