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2011•Journal of Bingtuan Education InstituteRequires access

Comparison and Analysis of Two Improved Schemes for Lagrange Interpolation

Guo Rui

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Abstract

Based on the Lagrange interpolation polynomial,two improved schemes for the Lagrange interpolation are proposed:Aitken interpolation and barycentric Lagrange interpolation.We compare the above schemes from the aspects of complexity and numerical stability.The results show that the barycentric Lagrange interpolation is optimal.In the end,we give the numerical experiments,and the numerical results implying the efficiency of the new scheme.

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What this paper is about

Based on the Lagrange interpolation polynomial,two improved schemes for the Lagrange interpolation are proposed:Aitken interpolation and barycentric Lagrange interpolation.We compare the above schemes from the aspects of complexity and numerical stability.The results show that the barycentric Lagrange interpolation is optimal.In the end,we give the numerical experiments,and the numerical results implying the efficiency of the new scheme.

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Available abstract

Based on the Lagrange interpolation polynomial,two improved schemes for the Lagrange interpolation are proposed:Aitken interpolation and barycentric Lagrange interpolation.We compare the above schemes from the aspects of complexity and numerical stability.The results show that the barycentric Lagrange interpolation is optimal.In the end,we give the numerical experiments,and the numerical results implying the efficiency of the new scheme.

Key concepts: Barycentric coordinate system, Lagrange polynomial, Interpolation (computer graphics), Trilinear interpolation, Inverse quadratic interpolation, Polynomial interpolation, Mathematics, Trigonometric interpolation

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