MAVKA: Program of statistically optimal determination of phenomenological parameters of extrema. Parabolic spline algorithm and analysis of variability of the semi-regular star Z UMa

Abstract

Advanced MAVKA software for the approximation of extrema observations is used\nto analyze the variability of the brightness of pulsating and eclipsing stars,\nbut may be useful in analyzing signals of any nature. A new algorithm using a\nparabolic (quadratic) spline is proposed. In contrast to the traditional\ndefinition of a spline as a piecewise-defined function at fixed intervals, a\nspline is proposed to be divided into three intervals, but the positions of the\nboundaries between the intervals are additional parameters. The spline defect\nis 1, that is, the function and its first derivative are continuous and the\nsecond derivative can be discontinuous at the boundaries. Such a function is an\nenhancement of the "asymptotic parabola" (Marsakova and Andronov 1996). The\ndependence of the fixed signal approximation accuracy on the location of the\nboundaries of the interval is considered. The parameter accuracy estimates\nusing the least squares method and bootstrap are compared. The variability of\nthe semi-regular pulsating star Z UMa is analyzed. The presence of\nmulticomponent variability of an object, including, four periodic oscillations\nand significant variability of the amplitudes and phases of individual\noscillations is shown.\n