A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions
Department of Mathematics, College of Natural Sciences, Cantho University, 3/2 Street, Cantho City, Vietnam
Math. Comput. Appl. 2018, 23(4), 63; https://doi.org/10.3390/mca23040063
Received: 13 August 2018
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Revised: 4 October 2018
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Accepted: 16 October 2018
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Published: 17 October 2018
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 with integrands of the form , another MAPLE procedure is proposed to find the desired polynomial estimates in norm for the best -approximation of the sine function in the vector space of polynomials of degree at most ℓ, a subspace of .
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Keywords:
approximation; approximate value; evaluation error; approximation error; piecewise approximate polynomial; rational approximation; Taylor’s Theorem
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MDPI and ACS Style
Quan, L.P. A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions. Math. Comput. Appl. 2018, 23, 63. https://doi.org/10.3390/mca23040063
AMA Style
Quan LP. A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions. Mathematical and Computational Applications. 2018; 23(4):63. https://doi.org/10.3390/mca23040063
Chicago/Turabian StyleQuan, Le P. 2018. "A Computational Method with MAPLE for a Piecewise Polynomial Approximation to the Trigonometric Functions" Mathematical and Computational Applications 23, no. 4: 63. https://doi.org/10.3390/mca23040063
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