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A Survey on Lagrange Interpolation Based on Equally Spaced Nodes

Michael Revers

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Abstract

Lagrange interpolation polynomials based on the equidistant node system have not been a popular subject in approximation theory. This is due to some famous examples published by C. Runge in 1901 and later by S.N. Bernstein in 1918 which discouraged mathematicians from considering this method of interpolation. This paper provides a brief survey of Lagrange interpolation polynomials which are based on equidistant nodes including recent results on pointwise divergence properties and certain limit relations.

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What this paper is about

Lagrange interpolation polynomials based on the equidistant node system have not been a popular subject in approximation theory. This is due to some famous examples published by C. Runge in 1901 and later by S.N. Bernstein in 1918 which discouraged mathematicians from considering this method of interpolation. This paper provides a brief survey of Lagrange interpolation polynomials which are based on equidistant nodes including recent results on pointwise divergence properties and certain limit relations.

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Available abstract

Lagrange interpolation polynomials based on the equidistant node system have not been a popular subject in approximation theory. This is due to some famous examples published by C. Runge in 1901 and later by S.N. Bernstein in 1918 which discouraged mathematicians from considering this method of interpolation. This paper provides a brief survey of Lagrange interpolation polynomials which are based on equidistant nodes including recent results on pointwise divergence properties and certain limit relations.

Key concepts: Equidistant, Interpolation (computer graphics), Mathematics, Pointwise, Lagrange polynomial, Limit (mathematics), Birkhoff interpolation, Applied mathematics

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