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Given a function f : R + R, real values a 0, the bisection method computes a sequence C1,C2, ... such that + c as
Given a function f : R + R, real values a 0, the bisection method computes a sequence C1,C2, ... such that + c as n +, where ce [a, b] with f(c) = 0. The algorithm stops when it finds some n e N such that - St. The bisection method computes the sequence by repeatedly bisecting the interval [a, b], hence the name. The algorithm can be expressed in pseudocode as follows. INPUT real-valued function f, a 0 OUTPUT real number 4 with Incl Se for some root c off SET , TO SET 6 TO SET , TO 1 WHILE bm- an>E SET CTO (Or+an)/2 IF f(c)=0 SET an+1 TO en SET bm+1 TOC ELSE IF f(an) f(en) 0, the bisection method computes a sequence C1,C2, ... such that + c as n +, where ce [a, b] with f(c) = 0. The algorithm stops when it finds some n e N such that - St. The bisection method computes the sequence by repeatedly bisecting the interval [a, b], hence the name. The algorithm can be expressed in pseudocode as follows. INPUT real-valued function f, a 0 OUTPUT real number 4 with Incl Se for some root c off SET , TO SET 6 TO SET , TO 1 WHILE bm- an>E SET CTO (Or+an)/2 IF f(c)=0 SET an+1 TO en SET bm+1 TOC ELSE IF f(an) f(en)
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