The point procedure PRZSS1 for the simultaneous estimation of the zeros of a polynomial

The order of convergence of the existing interval zoro symmetric single-step procedure is at least 4. The point version shares the same order of convergence. The point version of the interval zoro symmetric single-step procedure, aptly called point zoro symmetric single-step procedure, is modified by repeating the two forward and one backward steps r times. This modified procedure is named as point repeated zoro symmetric single-step procedure. It is shown that this procedure converges at the rate of at least 3r + 1 where r ≥ 1. This procedure and that of the point zoro symmetric single-step procedure are identical when r = 1. Numerical results show that the proposed point repeated zoro symmetric single-step procedure possesses higher rate of convergence than does the point zoro symmetric single-step procedure.

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