It is necessary to add one further set of instructions to this algorithm. We repeat the process with the new set until our stopping criterion is satisfied, as mentioned above. This completes one iteration of the method. 8.4 we replace x 0 by x 2 and x 2 by x 3. Next, we replace either x 0 or x 1 by x 2, exactly as in the regula falsi method, and replace x 2 by x 3. Only one of these, denoted by x 3, will be inside. The polynomial equation p 2( x) = 0 must then have real roots. We could select x 2 as the midpoint of or as the number obtained by one iteration of the secant method. This time we begin with numbers x 0 < x 1 such that f(x 0) f(x 1) < 0 and select x 2 as some number in. To avoid the possibility of the polynomial equation p 2( x) = 0 having complex roots, we may adopt a variant of the above method in which the root is bracketed at any stage.
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