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Example showing non-monotone cubic interpolation (in red) and monotone cubic interpolation (in blue) of a monotone data set. Monotone interpolation can be accomplished using cubic Hermite spline with the tangents m i {\displaystyle m_{i}} modified to ensure the monotonicity of the resulting Hermite spline.
The four Hermite basis functions. The interpolant in each subinterval is a linear combination of these four functions. On the unit interval [,], given a starting point at = and an ending point at = with starting tangent at = and ending tangent at =, the polynomial can be defined by = (+) + (+) + (+) + (), where t ∈ [0, 1].
In applied mathematics, an Akima spline is a type of non-smoothing spline that gives good fits to curves where the second derivative is rapidly varying. [1] The Akima spline was published by Hiroshi Akima in 1970 from Akima's pursuit of a cubic spline curve that would appear more natural and smooth, akin to an intuitively hand-drawn curve.
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the ...
A common spline is the natural cubic spline. A cubic spline has degree 3 with continuity C 2, i.e. the values and first and second derivatives are continuous. Natural means that the second derivatives of the spline polynomials are zero at the endpoints of the interval of interpolation. ″ = ″ =
The cubic B-spline is the cardinal B-spline of order 4, ... The following piecewise linear function is the approximation to ... (PDF). International ...
Estimation of the complete dose-response curve without any additional assumptions is usually done via linear interpolation between the point estimates. [ 3 ] Software for computing isotone (monotonic) regression has been developed for R , [ 4 ] [ 5 ] [ 6 ] Stata , and Python .
Spline interpolation — interpolation by piecewise polynomials Spline (mathematics) — the piecewise polynomials used as interpolants; Perfect spline — polynomial spline of degree m whose mth derivate is ±1; Cubic Hermite spline. Centripetal Catmull–Rom spline — special case of cubic Hermite splines without self-intersections or cusps