Understanding Akima Bivariate Interpolation: A Missing Piece in the Puzzle?

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SUMMARY

The discussion centers on the Akima bivariate interpolation method, originally proposed by H. Akima in 1974. Participants express frustration over the lack of detailed implementation guidance in Akima's original paper, specifically regarding the polynomial formulation needed for interpolation. While the derivatives are provided, the absence of a complete algorithm hampers effective application. Users are directed to the program available on Netlib, specifically at http://www.netlib.org/toms/474, for further assistance.

PREREQUISITES
  • Understanding of bivariate interpolation techniques
  • Familiarity with numerical methods and algorithms
  • Knowledge of derivative calculations in interpolation
  • Experience with accessing and utilizing resources from Netlib
NEXT STEPS
  • Research the implementation details of Akima's interpolation method
  • Explore numerical libraries that may include Akima interpolation, such as SciPy
  • Study polynomial interpolation techniques to understand the underlying mathematics
  • Investigate alternative bivariate interpolation methods for comparison
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Mathematicians, data scientists, and software developers interested in numerical analysis and interpolation methods will benefit from this discussion.

DrClaude
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Anyone familiar with the bivariate interpolation method developed by Akima?

I've been reading H. Akima, Commun. ACM 17, 18 (1974) and trying to implement his method, but he actually doesn't describe how to do the interpolation! The formulas for calculating the derivatives at each point are given, but not the polynomial that uses them for the interpolation.

I've been trying to reverse engineer his code, but it's starting to take too much of my time. Any help welcome.
 
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The links you gave are merely citations for the articles. If you want to view the contents, you must purchase a download. Sorry.
 
The program itself is available from netlib: http://www.netlib.org/toms/474

Otherwise, as I said, the algorithm is not completely described in the article.
 

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