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Advanced MAVKA software for the approximation of extrema observations is usedto analyze the variability of the brightness of pulsating and eclipsing stars,but may be useful in analyzing signals of any nature. A new algorithm using aparabolic (quadratic) spline is proposed. In contrast to the traditionaldefinition of a spline as a piecewise-defined function at fixed intervals, aspline is proposed to be divided into three intervals, but the positions of theboundaries between the intervals are additional parameters. The spline defectis 1, that is, the function and its first derivative are continuous and thesecond derivative can be discontinuous at the boundaries. Such a function is anenhancement of the "asymptotic parabola" (Marsakova and Andronov 1996). Thedependence of the fixed signal approximation accuracy on the location of theboundaries of the interval is considered. The parameter accuracy estimatesusing the least squares method and bootstrap are compared. The variability ofthe semi-regular pulsating star Z UMa is analyzed. The presence ofmulticomponent variability of an object, including, four periodic oscillationsand significant variability of the amplitudes and phases of individualoscillations is shown.

žurnal fìzičnih doslidženʹ/žurnal fìzičnih doslìdženʹ

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