  We introduce a special class of functions for mathematical modeling of
periodic signals of special shape with irregularly spaced arguments. This
method was developed for determination of phenomenological characteristics of
the light curves, which are necessary for registration in the "General
Catalogue of Variable Stars" and other databases. For eclipsing binary stars
with smooth light curves - of types EB and EW - it is recommended a
trigonometric polynomial of optimal degree in a complete or symmetric form. For
eclipsing binary systems with narrow minima (EA-type), statistically optimal is
an approximation in a class of non-polynomial spline functions. It is used a
combination of the second-order trigonometric polynomial (TP2, what describes
effects of "reflection", "ellipsoidality" and "spotness") and localized
contributions of minima (parametrized in depth and profile separately for
primary and secondary minima). Such an approach is characterized by a
statistical accuracy of the smoothing curve, which is up to ~1.5-2 times better
than the trigonometric polynomial of statistically optimal degree, and the
absence of false "waves" in the light curve associated with the effect of
Gibbs. In addition to the minimum width, which can not be determined by a
trigonometric polynomial approximation, the method allows to determine with
better accuracy its depth, as well as to separate the effects of the eclipse
and out-of-eclipse parts. For multi-color observations, improving the accuracy
of the smoothing of the curve in each filter will allow to obtain with better
accuracy the curves of the color index variations. Effectivity of the proposed
method increases with decreasing eclipse depth. The method called NAV ("New
Algol Variable"), was applied to eclipsing binary systems VSX
J022427.8-104034=USNO-B1.0 0793-0023471 and BM UMa. For VSX0224, an alternative
model of "double period" is discussed.
