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.

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.

单词	Broyden method
释义	Broyden method 英语百科 Broyden's method （重定向自Broyden method） 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.
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