On the backward stability of the second barycentric formula for interpolation
arXiv:1310.251622 citationsh-index: 12
Originality Incremental advance
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This resolves a long-standing open question about the numerical stability of a widely used interpolation method, benefiting numerical analysts and practitioners in scientific computing.
The paper proves that the second barycentric formula for interpolation is backward stable when the Lebesgue constant is small, providing a theoretical guarantee for its numerical reliability.
We present a new stability analysis for the second barycentric formula for interpolation, showing that this formula is backward stable when the relevant Lebesgue constant is small.