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

In summary, the conversation discusses the difficulties of implementing Akima's bivariate interpolation method, as it is not fully described in the article. The conversation also mentions that the program for the method is available from netlib.
  • #1
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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  • #2
The links you gave are merely citations for the articles. If you want to view the contents, you must purchase a download. Sorry.
 
  • #3
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.
 

1. What is Akima bivariate interpolation?

Akima bivariate interpolation is a method used to estimate the value of a function at a point within a given range of data points. It is specifically designed to interpolate between data points that do not follow a linear trend, such as noisy or scattered data.

2. What is the difference between Akima and other interpolation methods?

The main difference between Akima and other interpolation methods is that Akima takes into account the slope of the data points, whereas other methods only consider the value of the data points. This allows Akima to better handle noisy or scattered data and produce smoother interpolating curves.

3. How does Akima bivariate interpolation work?

Akima bivariate interpolation works by dividing the data points into smaller segments and fitting a piecewise cubic polynomial to each segment. The slope at each data point is then used to calculate the coefficients of the polynomial, which are then used to interpolate the value at the desired point.

4. When is Akima bivariate interpolation most useful?

Akima bivariate interpolation is most useful when dealing with data that does not follow a linear trend and may contain noise or scattered points. It is commonly used in scientific, engineering, and statistical applications to interpolate between data points and fill in missing values.

5. Are there any limitations to Akima bivariate interpolation?

Like any interpolation method, Akima bivariate interpolation is not without limitations. It is most effective when the data points are evenly distributed and there are no extreme outliers. It may also produce inaccurate results if the data points do not follow a smooth trend or if there are large gaps between data points.

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