📄 p21：对分法算例.htm
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<title>应用二分法求解非线性方程的计算过程显示页面</title>
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<h1>应用二分法求解非线性方程的计算过程显示页面</h1>
<br>
问题:<br>
求方程：x*x*x-x-1=0<br>
在区间：[a,b]=[1,2]<br>
内的近似解，绝对误差不超过：1e-8<br>
解： 变量说明如下：<br>
A[K]：第K次区间左端点；<br>
B[K]：第K次区间右端点；<br>
X[K]：第K次区间中点；<br>
Y[K]: 第K次区间中点函数值<br>
R[K]: 第K次区间长<br>
<br>
计算过程列表如下：</font>
<table bgColor="#3399ff" border="4" style="COLOR: #ffff00; FONT-SIZE: 24pt" width="120%">
<tbody>
<tr>
<td align="middle" width="10%">K</td>
<td align="middle" width="18%">A[K]</td>
<td align="middle" width="18%">B[K]</td>
<td align="middle" width="18%">X[K]</td>
<td align="middle" width="18%">Y[K]</td>
<td align="middle" width="18%">R[K]</td>
</tr>
<tr>
<td align="middle" width="10%">0</td>
<td align="right" width="18%">+1</td>
<td align="right" width="18%">+2</td>
<td align="right" width="18%">+1.5</td>
<td align="right" width="18%">+0.8750E0</td>
<td align="right" width="18%">+0.5000E0</td>
</tr>
<tr>
<td align="middle" width="10%">1</td>
<td align="right" width="18%">+1</td>
<td align="right" width="18%">+1.5</td>
<td align="right" width="18%">+1.25</td>
<td align="right" width="18%">-0.2969E0</td>
<td align="right" width="18%">+0.2500E0</td>
</tr>
<tr>
<td align="middle" width="10%">2</td>
<td align="right" width="18%">+1.25</td>
<td align="right" width="18%">+1.5</td>
<td align="right" width="18%">+1.375</td>
<td align="right" width="18%">+0.2246E0</td>
<td align="right" width="18%">+0.1250E0</td>
</tr>
<tr>
<td align="middle" width="10%">3</td>
<td align="right" width="18%">+1.25</td>
<td align="right" width="18%">+1.375</td>
<td align="right" width="18%">+1.3125</td>
<td align="right" width="18%">-0.5151E-1</td>
<td align="right" width="18%">+0.6250E-1</td>
</tr>
<tr>
<td align="middle" width="10%">4</td>
<td align="right" width="18%">+1.3125</td>
<td align="right" width="18%">+1.375</td>
<td align="right" width="18%">+1.34375</td>
<td align="right" width="18%">+0.8261E-1</td>
<td align="right" width="18%">+0.3125E-1</td>
</tr>
<tr>
<td align="middle" width="10%">5</td>
<td align="right" width="18%">+1.3125</td>
<td align="right" width="18%">+1.34375</td>
<td align="right" width="18%">+1.328125</td>
<td align="right" width="18%">+0.1458E-1</td>
<td align="right" width="18%">+0.1563E-1</td>
</tr>
<tr>
<td align="middle" width="10%">6</td>
<td align="right" width="18%">+1.3125</td>
<td align="right" width="18%">+1.328125</td>
<td align="right" width="18%">+1.320313</td>
<td align="right" width="18%">-0.1871E-1</td>
<td align="right" width="18%">+0.7813E-2</td>
</tr>
<tr>
<td align="middle" width="10%">7</td>
<td align="right" width="18%">+1.320313</td>
<td align="right" width="18%">+1.328125</td>
<td align="right" width="18%">+1.324219</td>
<td align="right" width="18%">-0.2128E-2</td>
<td align="right" width="18%">+0.3906E-2</td>
</tr>
<tr>
<td align="middle" width="10%">8</td>
<td align="right" width="18%">+1.324219</td>
<td align="right" width="18%">+1.328125</td>
<td align="right" width="18%">+1.326172</td>
<td align="right" width="18%">+0.6209E-2</td>
<td align="right" width="18%">+0.1953E-2</td>
</tr>
<tr>
<td align="middle" width="10%">9</td>
<td align="right" width="18%">+1.324219</td>
<td align="right" width="18%">+1.326172</td>
<td align="right" width="18%">+1.325195</td>
<td align="right" width="18%">+0.2037E-2</td>
<td align="right" width="18%">+0.9766E-3</td>
</tr>
<tr>
<td align="middle" width="10%">10</td>
<td align="right" width="18%">+1.324219</td>
<td align="right" width="18%">+1.325195</td>
<td align="right" width="18%">+1.324707</td>
<td align="right" width="18%">-0.4659E-4</td>
<td align="right" width="18%">+0.4883E-3</td>
</tr>
<tr>
<td align="middle" width="10%">11</td>
<td align="right" width="18%">+1.324707</td>
<td align="right" width="18%">+1.325195</td>
<td align="right" width="18%">+1.324951</td>
<td align="right" width="18%">+0.9948E-3</td>
<td align="right" width="18%">+0.2441E-3</td>
</tr>
<tr>
<td align="middle" width="10%">12</td>
<td align="right" width="18%">+1.324707</td>
<td align="right" width="18%">+1.324951</td>
<td align="right" width="18%">+1.324829</td>
<td align="right" width="18%">+0.4740E-3</td>
<td align="right" width="18%">+0.1221E-3</td>
</tr>
<tr>
<td align="middle" width="10%">13</td>
<td align="right" width="18%">+1.324707</td>
<td align="right" width="18%">+1.324829</td>
<td align="right" width="18%">+1.324768</td>
<td align="right" width="18%">+0.2137E-3</td>
<td align="right" width="18%">+0.6104E-4</td>
</tr>
<tr>
<td align="middle" width="10%">14</td>
<td align="right" width="18%">+1.324707</td>
<td align="right" width="18%">+1.324768</td>
<td align="right" width="18%">+1.324738</td>
<td align="right" width="18%">+0.8355E-4</td>
<td align="right" width="18%">+0.3052E-4</td>
</tr>
<tr>
<td align="middle" width="10%">15</td>
<td align="right" width="18%">+1.324707</td>
<td align="right" width="18%">+1.324738</td>
<td align="right" width="18%">+1.324722</td>
<td align="right" width="18%">+0.1848E-4</td>
<td align="right" width="18%">+0.1526E-4</td>
</tr>
<tr>
<td align="middle" width="10%">16</td>
<td align="right" width="18%">+1.324707</td>
<td align="right" width="18%">+1.324722</td>
<td align="right" width="18%">+1.324715</td>
<td align="right" width="18%">-0.1406E-4</td>
<td align="right" width="18%">+0.7629E-5</td>
</tr>
<tr>
<td align="middle" width="10%">17</td>
<td align="right" width="18%">+1.324715</td>
<td align="right" width="18%">+1.324722</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+0.2209E-5</td>
<td align="right" width="18%">+0.3815E-5</td>
</tr>
<tr>
<td align="middle" width="10%">18</td>
<td align="right" width="18%">+1.324715</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324717</td>
<td align="right" width="18%">-0.5925E-5</td>
<td align="right" width="18%">+0.1907E-5</td>
</tr>
<tr>
<td align="middle" width="10%">19</td>
<td align="right" width="18%">+1.324717</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">-0.1858E-5</td>
<td align="right" width="18%">+0.9537E-6</td>
</tr>
<tr>
<td align="middle" width="10%">20</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+0.1760E-6</td>
<td align="right" width="18%">+0.4768E-6</td>
</tr>
<tr>
<td align="middle" width="10%">21</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">-0.8408E-6</td>
<td align="right" width="18%">+0.2384E-6</td>
</tr>
<tr>
<td align="middle" width="10%">22</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">-0.3324E-6</td>
<td align="right" width="18%">+0.1192E-6</td>
</tr>
<tr>
<td align="middle" width="10%">23</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">-0.7823E-7</td>
<td align="right" width="18%">+0.5960E-7</td>
</tr>
<tr>
<td align="middle" width="10%">24</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+0.4886E-7</td>
<td align="right" width="18%">+0.2980E-7</td>
</tr>
<tr>
<td align="middle" width="10%">25</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">-0.1469E-7</td>
<td align="right" width="18%">+0.1490E-7</td>
</tr>
<tr>
<td align="middle" width="10%">26</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+1.324718</td>
<td align="right" width="18%">+0.1709E-7</td>
<td align="right" width="18%">+0.7451E-8</td>
</tr>
</tbody>
</table>
<font color="#ffcc00" face="楷体_GB2312" size="6"><br>
附：算法说明如下：<br>
A[0]=a;<br>
B[0]=b;<br>
X[0]=(a+b)/2;<br>
Y[0]=F(X[0]);<br>
R[0]=(b-a)/2;<br>
for(K=0;n<N;K++)<br>
{ if(Y[K]*Y[0]>0){A[K+1]=X[K];B[K+1]=B[K];}<br>
else {A[K+1]=A[K];B[K+1]=X[K];}<br>
X[K+1]=(A[K+1]+B[K+1])/2;<br>
Y[K+1]=F(X[K+1]);<br>
R[K+1]=X[K+1]-X[K];<br>
if(R[K+1]<EPS) break;<br>
}</font>
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