2007•Journal of Zhengzhou UniversityRequires access

Research on Emile Borel's Work on Improving Lagrange Interpolation Polynomial

Zhang We

Abstract

Lagrange interpolation polynomial is very useful in numerical analysis.But there exist functions for which the sequence of interpolation polynomial does not tend to them.This phenomenon is stated by Meray,Borel and Runge.It is analyzed by Borel in detail from the point of real variables.On the basis of reading original sources on this subject,Borel's background thought and method of improving Lagrange interpolation polynomial are discussed.Finally,the influence of his interpolation polynomial in the development of uniform approximation is discussed.

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Key concepts: Lagrange polynomial, Polynomial interpolation, Trigonometric interpolation, Mathematics, Interpolation (computer graphics), Birkhoff interpolation, Applied mathematics, Polynomial