Broyden's method
（重定向自Broyden method）
![The graph of a strictly concave quadratic function is shown in blue, with its unique maximum shown as a red dot. Below the graph appears the contours of the function: The level sets are nested ellipses.](/Images/godic/202501/02/Max_paraboloid.svg4334.png")
In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in k variables. It was originally described by C. G. Broyden in 1965.
Newton's method for solving f(x) = 0 uses the Jacobian matrix, J, at every iteration. However, computing this Jacobian is a difficult and expensive operation. The idea behind Broyden's method is to compute the whole Jacobian only at the first iteration, and to do a rank-one update at the other iterations.