Finding the best quadratic approximation of a function

• Autores: Yajun Yang
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 42, Nº. 6, 2011, págs. 812-823
• Idioma: inglés
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• Resumen

  • This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x)?=?ex. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact that three non-collinear points determine a unique quadratic function. Three different techniques for measuring the error in the approximations are considered.