Hiroshi Akima

Abstract: A method of interpolation that accurately interpolates data values that satisfy a function is said to have the accuracy of that function. The desired or required properties for a univariate interpolation method are reviewed, and the accuracy of a third–degree polynomial is found to be one of the desirable properties. A method of univariate interpolation having the accuracy of a third–degree polynomial while retaining the desirable properties of the method developed earlier by Akima( J. ACM 17, PP. 589–602, 1970) has been developed. The newly developed method is based on a piecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive intervals of the given data points. The method estimates the first derivative of the interpolating function (or the slope of the curve) at each given data point from the coordinates of seven data points. The resultant curve looks natural in many cases when the method is applied to curve fitting. The method is presented with examples. Possible use of a higher–degree polynomial in each interval is also examined.

Keywords: curve fitting; interpolation; polynomial; second curve fitting; second-degree polynomial; third-degree polynomial; univariate interpolation degree polynomial; univariate interpolation

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