Bisection and While Loops

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• Questions?
• Bisection Lab
  • How do while loops (or at least a while loop) fit into the bisection algorithm?
    

    bisection( f, xl, xu, es )
        xm = ( xl + xu ) / 2
        ea = es + 1
        while ea > es 
            if f(xm) f(xl) < 0
                xu = xm
            if f(xm) f(xl) > 0
                xl = xm 
            otherwise
                stop
            xn = ( xl + xu ) / 2
            ea = abs( ( xn - xm ) / xn )
            xm = xn
        end of while

    • Note that you can’t loop until f(x_m) = 0, because that might not happen in finite time
      
  • “Search” idiom for using while
    

    x = initial candidate
    while x does not satisfy search goal
        update x

• Next
  • If statements
  • Read sections 4.1 - 4.3

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