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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