Abstract—Zero-Error type of Chebyshev polynomials is one of Chebyshev polynomials extensions, it focus on “the zero error” and “the maximum absolute error minimization”. Under the condition of y(x) 0 , the existence question about Z-Chebyshev polynomials, which including the differential equations, the relevant definitions, the corresponding nature, the mathematical expressions, the recursive formula, the relationship between Z-Chebyshev polynomials and Chebyshev polynomials, are discussed and proved. Under the condition of y(x) 0 , the general features and characteristics about ZChebyshev polynomials in the process of being realized, the algorithm to obtain this approximation solution, are introduced and given.
Index Terms—Chebyshev, polynomials, prediction, optimal approximation.
Lemin Gu is with the Tongji University, China (e-mail: gulemin@tongji.edu.cn).
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Cite:Lemin Gu, "Zero-Error Type of Chebyshev Polynomials," International Journal of Modeling and Optimization vol. 3, no. 3, pp. 272-277, 2013.
