非线性方程组

IF 1.1 3区数学 Q2 MATHEMATICS, APPLIED Dynamics of Partial Differential Equations Pub Date : 2019-11-20 DOI:10.1201/9780429440908-10

V. Henner, T. Belozerova, A. Nepomnyashchy

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引用次数: 0

摘要

求解非线性方程f(x) = 0的牛顿方法可以推广到n维情况。变量的值和函数的值现在是n维向量，如果可以的话，我们把它们写成X和F (X)提醒我们它们不再是标量。由于我们的例子都是二维的，我们有时可以写成(x, y)而不是x。导数现在变成了雅可比矩阵(或者简单地说，“雅可比矩阵”)，我们将其写成nxn矩阵DF (x)。(i, j)项是

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Nonlinear Equations

Newton’s method for solving a nonlinear equation f(x) = 0 can be generalized to the n-dimensional case. The value of the variable and the value of the function are now n-dimensional vectors, and when we can, we will write these as X and F (X) to remind us that they are no longer scalars. Since our examples will all be two dimensional, we may sometimes write (x, y) instead of X. The derivative now becomes the jacobian matrix (or simply, “the jacobian”), which we will write as the n× n matrix DF (X). The (i, j) entry is

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来源期刊

Dynamics of Partial Differential Equations 数学-应用数学

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes novel results in the areas of partial differential equations and dynamical systems in general, with priority given to dynamical system theory or dynamical aspects of partial differential equations.