AbstractFor each natural number m greater than one, and each natural number k less than or equal to m, there exists a rootfinding iteration function, B (k) m defined as the ratio of two determinants that depend on the first m − k derivatives of the given function. This infinite family is derived in  and its order of convergence is analyzed in . In this paper we give a computational study of the first nine rootfinding methods. These include Newton, secant, and Halley methods. Our computational results with polynomials of degree up to 30 reveal that for small degree polynomials B (k−1) m is more efficient than B (k) m , but as the degree increases, B (k) m becomes more efficient than B (k−1) m . The most efficient of the nine methods is B (4) 4, having theoretical order of convergence equal to 1.927. Newton’s method which is often viewed as the method of choice is in fact the least efficient method.
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