It is very necessary to represent arbitrary function as a polynomial in many situations because polynomial has many valuable properties. Fortunately, any analytic function can be approximated by Taylor polynomial. The quality of Taylor approximation within given interval is dependent on degree of Taylor polynomial and the width of such interval. Taylor polynomial gains highly precise approximation at the point where the polynomial is expanded and so, the farer from such point it is, the worse the approximation is. Given two successive Taylor polynomials which are approximations of the same analytic function in given interval, this research proposes a method to improve the later one by minimizing their deviation so-called square error. Based on such method, the research also propose a so-called shifting algorithm which results out optimal approximated Taylor polynomial in given interval by dividing such interval into sub-intervals and shifting along with sequence of these sub-intervals in order to improve Taylor polynomials in successive process, based on minimizing square error.
展开▼
