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    I cant see if what you have written is right because I had no idea modulus was involved but I have just been playing around with some linear interpolation and from what I can see:

    If the curve is y=f(x) and the limits are a and b then the first approximation of the root, x_1 is given by:

    x_1=a-\frac{f(a)(b-a)}{f(b)-f(a)}

    The way I got to this was from thinking about what linear interpolation actually is.

    First, you take a curve and find an interval which has a root in it, say a<x<b

    Then draw a straight line from one end of the interval to the other i.e. join the points (a,f(a)) and (b,f(b))

    Finally work out where this straight line crosses the x axis and bingo, you have your approximation.
 
 
 
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Updated: November 9, 2008

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