Q2: Show that the iteration formula for the Secant Method applied to the equation x^2 - 5 = 0 to approximate its root ? can be expressed in the following form: x_{n+1} = frac{x_{n-1}x_n + 5}{x_{n-1} + x_n}.
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We have the equation $x^2 - 5 = 0$. Show more…
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The iteration equation of secant method given by x_{n+1} = x_n - f(x_n)(x_n - x_{n-1}) / (f(x_n) - f(x_{n-1})) can be written in simpler form x_{n+1} = (x_n f(x_n) - x_n f(x_{n-1}) - x_n f(x_n) + x_{n-1} f(x_n)) / (f(x_n) - f(x_{n-1})) = (x_{n-1} f(x_n) - x_n f(x_{n-1})) / (f(x_n) - f(x_{n-1})) Explain why, in general, this iteration equation is likely to be less accurate than the one given x_{n+1} = x_n - f(x_n)(x_n - x_{n-1}) / (f(x_n) - f(x_{n-1}))
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