Please use this identifier to cite or link to this item: https://dspace.ctu.edu.vn/jspui/handle/123456789/12645
Title: A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions
Authors: Lê, Phương Quân
Keywords: Approximation
Approximate value
Evaluation erro
Approximation error
Piecewise approximate polynomial
Rational approximation
Taylor’s Theorem
Issue Date: 2018
Series/Report no.: Mathematical and Computational Applications;23 .- p. 1-11
Abstract: A complete MAPLE procedure is designed to effectively implement an algorithm for approximating trigonometric functions. The algorithm gives a piecewise polynomial approximation on an arbitrary interval, presenting a special partition that we can get its parts, subintervals with ending points of finite rational numbers, together with corresponding approximate polynomials. The procedure takes a sequence of pairs of interval--polynomial as its output that we can easily exploit in some useful ways. Examples on calculating approximate values of the sine function with arbitrary accuracy for both rational and irrational arguments as well as drawing the graph of the piecewise approximate functions are presented. Moreover, from the approximate integration on [a,b] with integrands of the form xm\sinₓ, another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best L²-approximation of the sine function in the vector space Pl of polynomials of degree at most l, a subspace of L²(a,b).
URI: http://dspace.ctu.edu.vn/jspui/handle/123456789/12645
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