Academic Editor: Youssef EL FOUTAYENI
Received |
Accepted |
Published |
23 January 2020 |
07 February 2020 |
10 March 2020 |
Abstract: Given a strictly monotone cumulative function f : [a,b] → [c,d], with a, b, c, d ∈ R, a < b and c < d, such that f ([a,b]) = [c,d]. The use of spline approximation to approximate the inverse of f is natural in many applications, and it leads to schemes that are faster and simpler to implement than the inversion schemes based on iterative methods. We show that, with shape-preserving quadratic Hermite interpolation in B-spline representation, we can preserve the monotonicity of the inverse of f while maintaining third-order of the interpolation error. To demonstrate the effectiveness of this approach, we provide some examples of applications such as the inversion of cumulative distribution functions (arc-length and normal cumulative distributions) and the computation of the Lambert W-function.
