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)s⊤ks⊤ksk,where sk=xk+1−xk 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=xk−B−1kF(xk).