BibTeX
@ARTICLE{
         Bosse2019mfs,
       author = "T. Bosse",
       title = "({A}lmost) matrix-free solver for piecewise linear functions in abs-normal form",
       journal = "Numerical Linear Algebra with Applications",
       pages = "e2258",
       url = "https://onlinelibrary.wiley.com/doi/abs/10.1002/nla.2258",
       doi = "10.1002/nla.2258",
       abstract = "Summary The abs-normal form (ANF) is a compact algebraic representation for
         piecewise linear functions. These functions can be used to approximate piecewise smooth functions
         and contain valuable information about the nonsmoothness of the investigated function. The
         information helps to define step directions within general Newton methods that obey the structure of
         the original function and typically yield better convergence. However, the computation of the
         generalized Newton directions requires the solution of a piecewise linear equation in ANF. It was
         observed that the ANF can become very large, even for simple functions. Hence, if a solver is based
         on the ANF and uses the (Schur-complement) matrices of the explicit ANF representation, it has to be
         considered computationally expensive. In this paper, we will address this question and present the
         first (almost) matrix-free versions of some solver for ANFs. The theoretical discussion is supported
         by some numerical run-time experiments.",
       year = "2019",
       volume = "26",
       number = "5",
       ad_theotech = "Piecewise Linear"
}