THE HISTOGRAM DATA APPROXIMATION WITH THE CONDITIONAL MINIMIZATION METHOD FOR THE LENGTH OF THE CUBIC C1-CLASS SPLINE WITH THE NON-NEGATIVENESS AND LOCAL MONOTONICITY PROPERTIES. PART 1
S. V. Mzhachikh, N. V. Kolobyanina, Yu. N. Lapshina
VANT. Ser.: Mat. Mod. Fiz. Proc 2023. Вып.2. С. 30-44.
The paper considers the problem of processing the data which is available in the form of a function of a single variable given by a stepwise histogram. With such data approximation built in the form a cubic C1-class spline with the desired properties, possible, including non-negativeness and local monotonicity, the researcher can estimate the monotonicity sites and values at the given points, both for the function itself and for its derivative. The paper presents the fundamental principles of the approximation calculation method. The problem is solved with the method of minimizing the target function, which is the spline curve length dependence on the vector quantity. For the vector in question, a region is formed, which sets the required spline properties. The problem is solved most accurately with the use of limitations in the form of nonlinear inequalities, however, in some problems linear inequalities are also permitted. In the latter case, an approximate solution can be found, quickly and with no faults. Keywords: cubic spline, conditional minimization, locally monotone approximation, non-negative approximation, the modified Lagrangian method, the gradient descent method, the Newton linearization method, intragroup spectrum.
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