Divided Differences , Shift Transformations and Larkin ' s Root Finding Method
نویسنده
چکیده
For a one-dimensional complex-valued function/this paper deals with iterative root finding methods using divided differences of /. Assuming that / is given in a Newtonian representation we show how Homer-like transformations ("shift transformations") yield the divided differences needed in each iteration step. In particular, we consider an iteration method given by Larkin [5] and derive an equivalent version of this method fitting into this context. Monotonie convergence to real roots of real polynomials is investigated. Both "shift-" and "nonshift versions" of several root finding methods are tested and compared with respect to their numerical behavior.
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