在一个变量中求解非线性方程

这fzerofunction attempts to find a root of one equation with one variable. You can call this function with either a one-element starting point or a two-element vector that designates a starting interval. If you givefzero一个起点X0，，，，fzero首先搜索该函数更改符号的时间间隔。如果发现间隔，fzero返回附近函数更改符号的值。如果找不到这样的间隔，fzero返回南。Alternatively, if you know two points where the function value differs in sign, you can specify this starting interval using a two-element vector;fzero保证可以缩小间隔并返回符号更改附近的值。

以下各节包含两个示例，这些示例说明了如何使用起始间隔和起点来找到函数的零。示例使用该功能humps.m，，，，which is provided with MATLAB^®。这following figure shows the graph of驼峰。

X= -1:.01:2; y = humps(x); plot(x,y) xlabel('X'）；ylabel（'humps(x)'） 网格on

Using a Starting Interval

图驼峰表明该函数为负X= -1和积极的X= 1。您可以通过计算来确认驼峰在这两个点上。

驼峰(1)

一个ns = 16

驼峰（-1）

一个ns = -5.1378

Consequently, you can use[-1 1]作为开始间隔fzero。

迭代算法fzero发现越来越小的子间隔[-1 1]。对于每个子间隔，驼峰differs at the two endpoints. As the endpoints of the subintervals get closer and closer, they converge to zero for驼峰。

显示进度fzero在每次迭代中，设置展示option to迭代using the最佳集功能。

选项=最佳集（'Display'，，，，'iTer'）；

然后致电fzero一个s follows:

一个= fzero(@humps,[-1 1],options)

Func-count x f(x) Procedure 2 -1 -5.13779 initial 3 -0.513876 -4.02235 interpolation 4 -0.513876 -4.02235 bisection 5 -0.473635 -3.83767 interpolation 6 -0.115287 0.414441 bisection 7 -0.115287 0.414441 interpolation 8 -0.132562 -0.0226907 interpolation 9 -0.131666 -0.0011492 interpolation 10 -0.131618 1.88371e-07 interpolation 11 -0.131618 -2.7935e-11 interpolation 12 -0.131618 8.88178e-16 interpolation 13 -0.131618 8.88178e-16 interpolation Zero found in the interval [-1, 1]

a = -0.1316

每个值Xrepresents the best endpoint so far. The程序column tells you whether each step of the algorithm uses bisection or interpolation.

You can verify that the function value at一个通过输入接近零

的线条(a)

ANS = 8.8818e-16

使用起点

假设您不知道两个点的功能值驼峰differ in sign. In that case, you can choose a scalarX0一个s the starting point forfzero。fzerofirst searches for an interval around this point on which the function changes sign. Iffzero找到这样的间隔，它以上一节中描述的算法进行。如果找不到这样的间隔，fzero返回南。

For example, set the starting point to-0.2， 这展示option to迭代，，，，一个nd callfzero：

选项=最佳集（'Display'，，，，'iTer'）；a = fzero（@humps，-0.2，选项）

Search for an interval around -0.2 containing a sign change: Func-count a f(a) b f(b) Procedure 1 -0.2 -1.35385 -0.2 -1.35385 initial interval 3 -0.194343 -1.26077 -0.205657 -1.44411 search 5 -0.192 -1.22137-0.208 -1.4807 search 7 -0.188686 -1.16477 -0.211314 -1.53​​167 search 9 -0.184 -1.08293 -0.216 -1.60224 search 11 -0.177373 -0.963455 -0.222627 -1.69911 search 13 -0.168 -0.786636 -0.232 -1.83055 search 15 -0.154745 -0.51962-0.245255 -2.00602搜索17 -0.136 -0.104165 -0.264 -2.23521搜索18 -0.10949 0.572246 -0.264 -2.23521搜索搜索在此间隔[-0.10.10949，-0.264]中搜索为零，0.572246 initial 19 -0.140984 -0.219277 interpolation 20 -0.132259 -0.0154224 interpolation 21 -0.131617 3.40729e-05 interpolation 22 -0.131618 -6.79505e-08 interpolation 23 -0.131618 -2.98428e-13 interpolation 24 -0.131618 8.88178e-16 interpolation 25 -0.131618 8.88178E-16在间隔[-0.10949，-0.264]中发现的插值零

a = -0.1316

每个迭代时当前子间隔的终点都在标题下列出一个一个ndb，，，，while the corresponding values of驼峰在端点处列出f(a)一个ndf（b）， 分别。

在前九个步骤中，驼峰is negative at both endpoints of the current subinterval, which is shown in the output. At the tenth step, the sign of驼峰在端点上是积极的，-0.10949，但端点为负-0.264。从这一点开始，算法继续缩小间隔[-0.10949 -0.264]，，，，一个s described in the previous section, until it reaches the value-0.1316。