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On the abs-polynomial expansion of piecewise smooth functions
ArticleAbstract: Tom Streubel has observed that for functions in abs-normal form, generalized Taylor expansions of arPalabras claves:abs-linear form, abs-normal form, absolute convergence, forward mode propagation, Moore recurrences, Nonsmooth Taylor polynomial/series, quadratic complexityAutores:Andreas Griewank, Streubel T., Tischendorf C.Fuentes:scopusIntegrating Lipschitzian dynamical systems using piecewise algorithmic differentiation
ArticleAbstract: In this article we analyse a generalized trapezoidal rule for initial value problems with piecewisePalabras claves:65L05, 65L06, 65L70, 65L99, 65P10, Automatic differentiation, dense output, energy preservation, Lipschitz continuity, nonsmooth, Piecewise linearization, trapezoidal ruleAutores:Andreas Griewank, Hasenfelder R., Lehmann L., Radons M., Streubel T.Fuentes:scopusPiecewise linear secant approximation via algorithmic piecewise differentiation
ArticleAbstract: It is shown how piecewise differentiable functions F:ℝ n ↦ℝ m that are defined by evaluation programPalabras claves:49J52, 65D25, 65K10, ADOL-C, Automatic differentiation, generalized hermite interpolation, generalized Newton's method, Lipschitz continuity, stable piecewise linearizationAutores:Andreas Griewank, Hasenfelder R., Lehmann L., Radons M., Streubel T.Fuentes:scopusRepresentation and analysis of piecewise linear functions in abs-normal form
ArticleAbstract: It follows from the well known min/max representation given by Scholtes in his recent Springer book,Palabras claves:Algorithmic differentiation (AD), Complementary piecewise linear system (CLP), Equation solving, Linear complementarity (LCP), Piecewise linearization (PL), Semi-smooth newton, Smooth dominanceAutores:Andreas Griewank, Bernt J., Radons M., Streubel T.Fuentes:scopusSolving piecewise linear systems in abs-normal form
ArticleAbstract: With the ultimate goal of iteratively solving piecewise smooth (PS) systems, we consider the solutioPalabras claves:coherent orientation, Complementary system, Generalized Jacobian, Partial contractivity, Semismooth Newton, Sign real spectral radius, Switching depthAutores:Andreas Griewank, Bernt J., Radons M., Streubel T.Fuentes:scopus