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2012•Journal of Huzhou Teachers CollegeRequires access

Solving the 3n+2 Orders Hermite Interpolation Problems with the Method of Difference Quotient

Jing Cai

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Abstract

This paper mainly considers the Hermite interpolation problems with the method of divided difference at the same node.Based on the existing results,it studies the Hermite interpolation functions with derivative whose number of nodes is completely matching,builds some Hermite interpolating formulas with derivatives,and also gives the corresponding error estimate.Some numerical examples are presented to compare the proposed method with the existing Lagrange primary function method to show its advantage.

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What this paper is about

This paper mainly considers the Hermite interpolation problems with the method of divided difference at the same node.Based on the existing results,it studies the Hermite interpolation functions with derivative whose number of nodes is completely matching,builds some Hermite interpolating formulas with derivatives,and also gives the corresponding error estimate.Some numerical examples are presented to compare the proposed method with the existing Lagrange primary function method to show its advantage.

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Available abstract

This paper mainly considers the Hermite interpolation problems with the method of divided difference at the same node.Based on the existing results,it studies the Hermite interpolation functions with derivative whose number of nodes is completely matching,builds some Hermite interpolating formulas with derivatives,and also gives the corresponding error estimate.Some numerical examples are presented to compare the proposed method with the existing Lagrange primary function method to show its advantage.

Key concepts: Hermite interpolation, Cubic Hermite spline, Mathematics, Interpolation (computer graphics), Hermite polynomials, Birkhoff interpolation, Hermite spline, Monotone cubic interpolation

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