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Broyden’s Good Method

Let Bk be the approximation of the Jacobian Jk at iteration k. The update rule for Bk is:

Bk+1=Bk+(F(xk+1)F(xk)Bksk)sksksk,

where sk=xk+1xk is the step vector. The new approximation Bk+1 satisfies the **secant equation:

Bk+1sk=F(xk+1)F(xk).

The solution is updated as:

xk+1=xkB1kF(xk).