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The root of p 1(x) is x 1 f(x 0)f0(x 0)(x 1 −x 0) = 0 ie, x 1 = x 0 − f(x 0) f0(x 0) 3 Rootfinding Math 1070 > 3 Rootfinding > 32 Newton’s method Since x 1 is expected to be an improvement over x 0 as an estimate of α, we repeat the procedure with x 1 as initial guess x 2 = x 1 − f(x 1) f0(x 1) Repeating this process, we obtain a sequence of numbers, iterates, x 1,x 2,x 3.
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