# 1 Bisection

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NUMERICAL METHODS
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1 Basis of Bisection Method Theorem   x   f(x) x u  x  An equation f(x)=0, where f(x) is a real continuous function, has at least one root between x l and x u if f(x l ) f(x u ) < 0. Figure 1  At least one root exists between the two points if the function is real, continuous, and changes sign.    x   f(x) x u  x 2 Basis of Bisection Method Figure 2 If function does not change sign between two points, roots of the equation may still exist between the two points.    x f     0   x f      x   f(x) x u  x 3 Basis of Bisection Method Figure 3 If the function does not change sign between two points, there may not be any roots for the equation between the two points.   x   f(x) x u  x    x f     0   x f      x   f(x) x u  x 4 Basis of Bisection Method Figure 4 If the function changes sign between two points, more than one root for the equation may exist between the two points.    x f     0   x f

Apr 16, 2018

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