- Method
- References
In applied mathematics, an Akima spline is a type of cubic spline that is relatively robust to outliers.[1] The Akima spline was published by Hiroshi Akima in 1970.[2]
Method
Given a set of points 
, where the 
are strictly increasing, the Akima spline will go through each of the given points. At those points, its slope, 
, is a function of the locations of the points 
through 
. Specifically, we define 
as the slope of the line segment from to 
, namely 
. Then, is defined as the following weighted average of 
and :
The spline is then defined as the piecewise cubic function whose value between and 
is the unique cubic polynomial 
that satisfies the four constraints: 
, 
, 
, and 
.
References
1. ^{{Cite web|url=http://www.alglib.net/interpolation/spline3.php#header5|title=Spline interpolation and fitting – ALGLIB, C++ and C# library|website=www.alglib.net}}
2. ^http://www.leg.ufpr.br/lib/exe/fetch.php/wiki:internas:biblioteca:akima.pdf
{{math-stub}}2. ^http://www.leg.ufpr.br/lib/exe/fetch.php/wiki:internas:biblioteca:akima.pdf
1 : Splines (mathematics)
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