Modeling, Reproduction, and Mapping of Geofields With and Without Measurement Noise. Part 6. Piecewise Polynomial Approximations, Statistical Design of Experiments, and the Construction of Contour Maps

A. M. Pashayev; R. A. Sadykhov; S. B. Habibullayev

doi:10.1007/s11018-018-1395-4

Modeling, Reproduction, and Mapping of Geofields With and Without Measurement Noise. Part 6. Piecewise Polynomial Approximations, Statistical Design of Experiments, and the Construction of Contour Maps

Authors: Pashayev A.M.¹, Sadykhov R.A.¹, Habibullayev S.B.¹
Affiliations:
1. National Academy of Aviation of Azerbaijan
Issue: Vol 61, No 2 (2018)
Pages: 104-115
Section: Article
URL: https://journals.rcsi.science/0543-1972/article/view/246394
DOI: https://doi.org/10.1007/s11018-018-1395-4
ID: 246394

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Abstract
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Supplementary files
Statistics

Abstract

Spline, finite element, and piecewise polynomial fits of the boundaries of geofields with automatic matching are examined. The unknown coefficients of the approximating polynomials are estimated using measurements of their input and output coordinates in the presence of measurement noise. A new method for constructing contour maps is developed on the basis of the fundamental “recurrence” theorem of Poincare. The capabilities of this method for constructing contours are examined.