|
In calculus, Newton's method is an iterative method for finding the roots of a differentiable function (i.e. solutions to the equation ). In optimization, Newton's method is applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to ), also known as the stationary points of . ==Method== In the one-dimensional problem, Newton's method attempts to construct a sequence from an initial guess that converges towards some value satisfying . This is a stationary point of . The second order Taylor expansion of around is: :. We want to find such that is maximum. We seek to solve the equation that sets the derivative of this least expression with respect to equal to zero: :. For the value of , which is the solution of this equation, it can be hoped that will be closer to a stationary point . Provided that is a twice-differentiable function and other technical conditions are satisfied, the sequence will converge to a point satisfying . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「newton's method in optimization」の詳細全文を読む スポンサード リンク
|