A Recursive Descent Algorithm for Finding the Optimal Minimax Piecewise Linear Approximation of Convex Functions - Imamoto, A.; Tang, B. (2008 World Congress on Engineering and Computer Science, 2008)
The optimal minimax solution to the N segment piecewise linear approximation of arbitrary convex differentiable functions over a finite range is described. The optimal solution is uniquely described by the derivatives at N distinct points. The optimality of the solution is proven and a recursive descent algorithm is proposed. The efficacy of the algorithm and optimality of the solution are demonstrated in example solutions for commonly used functions.