Bracketing Methods (Bisection Method)

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Presentation transcript:

Bracketing Methods (Bisection Method) Faculty of Applied Engineering and Urban Planning Civil Engineering Department ECGD3110 Numerical Analysis Root Finding Bracketing Methods (Bisection Method) Lecture 1 1st Semester 2009/2010 UP Copyrights 2009

Content Solution Methods Graphical Methods Bracketing Methods Bisection Method

General Cases

Roots Solution with Bracketing Methods It is a simple technique for obtaining an estimate of root for the equation f(x)=0. It gives a rough approximation of the root solution(s)

The Bisection Method Choose lower xl and upper xu with: f(xl)f(xu)<0 Estimate of the root Check: If f(xl)f(xr)<0 the root between xl & xr If f(xl)f(xr)>0 the root between xu & xr If f(xl)f(xr)=0 the root is xr

Example Solve: Y=X3 – 5 using the bisection method

X  1.71

Example Solve: Y=X3 - 5 Solution

Bisection Method

True value = approximation + Error Et = true value – approximation When using the iterative approach to compute an answer and there is no true solution:

Error Estimates for Bisection Estimated solution in each iteration

Find the positive root knowing that it is between (0.5) and (1.5)

ϵa < ϵs Define xL, and xu Calculate xr xL = xr xu = xr End f(xL)f(xu) < 0 No Yes Calculate xr f(xL)f(xr) < 0 Yes No xL = xr xu = xr ϵa < ϵs No Yes End