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In this paper we present an algorithm to obtain the parameter planes offamilies of root-finding methods with several free critical points. Theparameter planes show the joint behaviour of all critical points. Thisalgorithm avoids the inconsistencies arising from the relationship between thedifferent critical points as well as the indeterminacy caused by the squareroots involved in their computation.  We analyse the suitability of this algorithm by drawing the parameter planesof different Newton-like methods with two and three critical points. We alsopresent some results of the expressions of the Newton-like operators and theirderivatives in terms of palindromic polynomials, and we show how to obtain theexpression of the critical points of a Newton-like method with realcoefficients.

Computing parameter planes of iterative root-finding methods with several free critical points