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Article information
2017 , Volume 22, ¹ 2, p.99-114
Popova O.A.
Application of numerical probabilistic analysis in interpolation problems
The paper addresses the application of numerical probabilistic analysis for construction of function approximations under conditions of stochastic uncertainty. We introduced the definitions of random interpolation and random spline in this study. To define these concepts we use the probabilistic extensions as the base component for numerical probabilistic analysis. To construct these extensions the arithmetical operations for probability density functions of the random variables and numerical procedures for the probabilistic extensions have been applied. Lagrange interpolation polynomials and polynomial splines with input random data are discussed. To employ the numerical probabilistic analysis we propose the special class of the random Lagrange interpolating polynomials. We argue that our approach to uncertainty representation allows us to build reliable estimates for random functions. In the case of a random piecewise linear interpolation we assess the accuracy of the mathematical expectation and variance. To use the numerical probabilistic analysis we proposed special class of the random cubic splines. For the construction of the random splines we solved the random system of linear algebraic equations. Our study shows that the application of the random splines for approximation of distribution functions and probability densities and allows the reliable estimate. This approach is based on the properties of order statistics. Reliable estimates are represented as the histogram P-boxes and second order histograms. To demonstrate our theory we use numerical examples to build the histogram P-boxes and the second order histogram. It is important to note that numerical results show the effectiveness of our techniques to small samples.
[full text]
Keywords: numerical probabilistic analysis, functions of random variables, interpolation, verified bounds
Author(s):
Popova Olga Arkadievna
PhD. , Associate Professor
Position: Associate Professor
Office: Institute of Space and Informatic Technologies Siberian Federal University
Address: 660041, Russia, Krasnoyarsk, 79 Svobodny pr.
E-mail: OlgaArc@yandex.ru
SPIN-code: 5635-7451 References:
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Bibliography link:
Popova O.A. Application of numerical probabilistic analysis in interpolation problems // Computational technologies. 2017. V. 22. ¹ 2. P. 99-114
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