Answer to Question #103594 in Quantitative Methods for Remi

Question #103594
Perform 6 iteration to find zero of the equation: x+3=e^x using bisection algorithm. How many steps of the algorithm are needed to compute toot of the equation?
1
Expert's answer
2020-02-24T11:38:41-0500

Solution. We write the equation in the form


"x+3-e^x=0"

Using for bisection algorithm for function f(x)=x+3-e^x.

Choose a and b such that f (a)> 0 and f (b) <0 (or vice versa). Find value c that equal to


"c=\\frac {a+b}{2}"

Choose a and b such that f(a)> 0 and f (b) <0 (or vice versa). Find c


"c=\\frac {a+b}{2}"

Find f(c). If f(c) =0 therefore c is root of equation f(x)=0. If f(c) ≠ 0 we check the sign of f(c).

If f(c) has the same sign as f(a) we replace a with c and we keep the same value for b.

If f(c) has the same sign as f(b), we replace b with c and we keep the same value for a.

The algorithm ends when the values of f(c) is less than a defined tolerance.

The number of iterations n needed to converge towards a root within the imposed tolerance Ɛ is calculated as:


"n\\eqslantgtr log_2(\\frac{b-a}{\u0190})"

The equation x+3-e^x=0 has two roots.

Let's make two tables with 6 iterations for each case.





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