# Brents Algorithm Assignment Help

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## What is Brents Algorithm?

1) Combines bracketing, bisection, and inverse quadratic interpolation.

2) Guaranteed to converge, but speed can vary with function and quality of initial guess.

3) Algorithm:

• Compute ‘f(x)’, ‘f(y)’, ‘f(z)’
• Compute A, B, C, D, E
• Let [y -> y + (A/B)]
• Repeat as [f(y) -> 0] C = [ f(y) / f(z) ]

D = [ f(y) / f(x)]

E = [ f(x) / f(z)]

A = D [ E(C - E) (z - y) – (1 - C)(y - x)]

B = [(E - 1)(C - 1)(D - 1)]

 Brent_method [v0_, w0_] =module [{ v = N[v0], w = N[w0], k },(fv = f[w]); (fw = f[w]);k = 0 ;label [int];x = v; fx = fv; y = z = (w - v);label [ext];if [abs [fx]