ANALYSIS AND SYNTHESIS OF THE CHEBYSHEV POLYNOMIALS IN THE REGRESSION ANALYSIS PROBLEMS
The article presents the strict mathematical analysis of synthesis of the multidimensional orthogonal polynomials, or the Chebyshev polynomials, aimed to improve stability of approximated regression relationships. The authors prove the theories of linear span properties, polynomial regression space and the stability of orthogonal basic sets of the Chebyshev polynomials constructed using the Gram–Schmidt algorithm.