0=F(X), for a solution vector X which involves choosing a starting value X0 and iterating Xn+1=Xn−[F′(Xn)+σnDiagF′(Xn)]−1F(Xn). In this iteration, at least one σn is a number greater than 0. Preferably, σn=min{β/n, [αn/(1+nαn)]∥F(Xn)∥}, where β is a constant that remains fixed for all n, and αn=∥F(Xn)∥/∥F(Xn−1)∥. "/>
Simulation of processes, devices and circuits by a modified newton method
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Simulation of processes, devices and circuits by a modified newton method
Simulation of processes, devices and circuits by a modified newton method
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机译：通过改进的牛顿法模拟过程，设备和电路
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摘要
Roughly described, a method for numerically solving a system of equations of the form 0=F(X), for a solution vector X which involves choosing a starting value X0 and iterating Xn+1=Xn−[F′(Xn)+σnDiagF′(Xn)]−1F(Xn). In this iteration, at least one σn is a number greater than 0. Preferably, σn=min{β/n, [αn/(1+nαn)]∥F(Xn)∥}, where β is a constant that remains fixed for all n, and αn=∥F(Xn)∥/∥F(Xn−1)∥.
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机译：粗略地描述了一种数字形式的方程组的求解方法<？in-line-formulae description =“在线表达式” end =“ lead”？> 0 = F （ X ），<？in-line-Formulae description =“ In-line Formulae” end =“ tail”？>求解矢量X，其中涉及选择起始值X 0 并进行迭代<？in-line-formulae description =“在线公式” end =“ lead”？> X n + 1 = X < Sub> n − [F '（ X n ）+σ n DiagF ′（ X n ）] -1 F （ X n ）。 <？in-line-formulae description =“在线公式” end =“ tail”？>在此迭代中，至少一个σ n 是一个大于0的数。<？in-line-formulae description =“在线公式” end =“ lead”？>σ n = min {β/ n，[αn /（1 + nα n ）]∥ F （ X n ）∥}，< ？in-line-formulae description =“在线公式” end =“ tail”？>其中β是一个常数，对于所有n都是固定的，并且<？in-line-formulae description =“在线公式” end =“ lead”？>α n =∥F（ X n ）∥/∥ F （ X n-1 ）∥。 <？in-line-formulae description =“在线公式” end =“ tail”？>
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