# Piecewise linear secant approximation via algorithmic piecewise differentiation

@article{Griewank2018PiecewiseLS, title={Piecewise linear secant approximation via algorithmic piecewise differentiation}, author={Andreas Griewank and Thomas Streubel and Lutz Lehmann and Manuel Radons and Richard Hasenfelder}, journal={Optimization Methods and Software}, year={2018}, volume={33}, pages={1108 - 1126} }

It is shown how piecewise differentiable functions F:ℝn↦ℝm that are defined by evaluation programmes can be approximated locally by a piecewise linear model based on a pair of sample points . We show that the discrepancy between function and model at any point x is of the bilinear order . As an application of the piecewise linearization procedure we devise a generalized Newton's method based on successive piecewise linearization and prove for it sufficient conditions for convergence and…

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