数值计算方法matlab例子.htm

数值计算方法

<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">2.0000</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT face="Times New Roman">&nbsp;<SPAN lang=EN-US><o:p></o:p></SPAN></FONT></P></TD>
<TD style="BORDER-RIGHT: windowtext 0.5pt solid; PADDING-RIGHT: 5.4pt; BORDER-TOP: #ece9d8; PADDING-LEFT: 5.4pt; PADDING-BOTTOM: 0cm; BORDER-LEFT: #ece9d8; WIDTH: 171pt; PADDING-TOP: 0cm; BORDER-BOTTOM: windowtext 0.5pt solid; BACKGROUND-COLOR: transparent; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt" vAlign=top width=228>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">1.0000<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>1.0000<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>1.0000<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>1.0000</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.9956<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.9958<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.9641<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.9947</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.9824<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.9831<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.9282<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.9797</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.9608<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.9624<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.8924<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.9561</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">… …</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.4718<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.4626<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.4995<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.4836</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.4185<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.4062<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.4523<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.4329</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.3679<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.3531<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.4051<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.3837</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">… …</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.0773<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.1292<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.1087<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.0534</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.0622<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.1271<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.0937<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.0347</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">… …</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.0238<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.0685<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.0334<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.0104</FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman">0.0183<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>0.0183<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.0183<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>0.0183</FONT></SPAN></P></TD></TR></TBODY></TABLE>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=3><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Courier New'; mso-hansi-font-family: 'Courier New'">将三种插值结果</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">y1,y2,y3</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">与精确值</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">y</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">项比较，显然</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">y1</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">在节点处不光滑</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">,</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">拉格朗日插值出现较大的振荡</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">,</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">样条插值得结果是最好的</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">.</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">增加</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">n</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">值（使</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">n=11</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">），再运行以上程序，得到的图形如右图所示，比较这两个图可发现，节点增加后，三种插值方法结果的准确度均有所提高，因此可近似地认为：增加节点个数可以提高插值结果的准确程度。</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21pt"><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋"><FONT size=3><FONT face="Times New Roman">&nbsp;<o:p></o:p></FONT></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=3><FONT face="Times New Roman"><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">第</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">3</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">题</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋"><o:p></o:p></SPAN></FONT></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21pt"><FONT size=3><FONT face="Times New Roman"><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">用给定的多项式，如</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">y=x<SUP>3</SUP>-6x<SUP>2</SUP>+5x-3</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">，产生一组数据</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">（</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">x<SUB>i</SUB>,y<SUB>i</SUB>,i=1,2,</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">…</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">,n</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">，再在</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">yi</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">上添加随机干扰</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">（</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">可用</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">rand</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">产生</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">（</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">0</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">，</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">1</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">均匀分布随机数，或用</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">randn</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">产生</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">N</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">（</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">0</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">，</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">1</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">）</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">分布随机数），然后用</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">x<SUB>i</SUB></SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">和添加了随机干扰的</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">y<SUB>i</SUB></SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">作</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">3</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">次多项式拟合，与原系数比较。如果作</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">2</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">或</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">4</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 楷体_GB2312">次多项式拟合，结果如何？</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; FONT-FAMILY: 仿宋_GB2312; mso-bidi-font-size: 10.0pt; mso-fareast-font-family: 华文仿宋"><o:p></o:p></SPAN></FONT></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21pt"><v:group id=_x0000_s1027 style="MARGIN-TOP: 8.25pt; Z-INDEX: -3; LEFT: 0px; MARGIN-LEFT: 153pt; WIDTH: 279pt; POSITION: absolute; HEIGHT: 218.4pt; TEXT-ALIGN: left" coordsize="5580,4368" o:allowincell="f" coordorigin="5040,10020"><v:shape id=_x0000_s1028 style="LEFT: 5040px; WIDTH: 5580px; POSITION: absolute; TOP: 12048px; HEIGHT: 2340px" type="#_x0000_t75"><v:imagedata o:title="" src="file&#58///C:/DOCUME~1/LIZHAO~1/LOCALS~1/Temp/msoclip1/01/clip_image003.emz"><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape><v:shape id=_x0000_s1029 style="LEFT: 5040px; WIDTH: 5580px; POSITION: absolute; TOP: 10020px; HEIGHT: 2184px" type="#_x0000_t75"><v:imagedata o:title="" src="file&#58///C:/DOCUME~1/LIZHAO~1/LOCALS~1/Temp/msoclip1/01/clip_image004.emz"><FONT face="Times New Roman" size=3></FONT></v:imagedata></v:shape></v:group><FONT size=3><FONT face="Times New Roman"><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">解：</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">2<o:p></o:p></SPAN></FONT></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 21pt"><FONT size=3><FONT face="Times New Roman"><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">编制</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋">y_2_3.m</SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'">文件</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 华文仿宋"><o:p></o:p></SPAN></FONT></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>n=15;<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>x=0:8/(n-1):8;<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>y=x.^3-6*x.^2+5*x-3;<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>z=0*x;<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>y0=y+rand(1,15);<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>f=polyfit(x,y0,m);<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>r=polyval(f,x)<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>pl2ot(x,z,<SPAN style="COLOR: maroon">'k'</SPAN>,x,y,<SPAN style="COLOR: maroon">'r:'</SPAN>,x,<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>r,<SPAN style="COLOR: maroon">'b'</SPAN>)<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><FONT size=3><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN></SPAN><SPAN style="FONT-FAMILY: 华文仿宋; mso-ascii-font-family: 'Times New Roman'"><FONT face="Times New Roman">程序及运行结果如下：</FONT></SPAN><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><SPAN style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </SPAN><SPAN style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</SPAN><o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>m=2 ,y_2_3<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>f =<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>5.9888<SPAN style="mso-spacerun: yes">&nbsp; </SPAN>-31.9916<SPAN style="mso-spacerun: yes">&nbsp; </SPAN><o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 18.0pt 36.0pt 54.0pt 72.0pt 90.0pt 108.0pt 126.0pt 144.0pt 162.0pt 180.0pt 198.0pt 216.0pt 234.0pt 252.0pt 270.0pt 288.0pt 306.0pt 324.0pt 342.0pt 360.0pt 378.0pt 396.0pt 414.0pt 432.0pt 450.0pt 468.0pt 486.0pt 504.0pt 522.0pt 540.0pt 558.0pt 576.0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3><SPAN style="mso-spacerun: yes">&nbsp;</SPAN>17.6679<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>m=3 ,y_2_3<SPAN style="COLOR: blue"><o:p></o:p></SPAN></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none"><v:shape id=_x0000_s1030 style="MARGIN-TOP: 7.8pt; Z-INDEX: -2; LEFT: 0px; MARGIN-LEFT: 162pt; WIDTH: 279pt; POSITION: absolute; HEIGHT: 117pt; TEXT-ALIGN: left" o:allowincell="f" type="#_x0000_t75"><v:imagedata o:title="" src="file&#58///C:/DOCUME~1/LIZHAO~1/LOCALS~1/Temp/msoclip1/01/clip_image006.emz"><FONT size=3></FONT></v:imagedata></v:shape><SPAN lang=EN-US style="COLOR: blue; FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>f =<SPAN style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </SPAN>0.9850<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>-5.8326 <o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt 69pt; TEXT-INDENT: -53.25pt; tab-stops: list 69.0pt; mso-list: l2 level2 lfo1; mso-layout-grid-align: none"><SPAN lang=EN-US style="COLOR: blue; FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>4.5549</FONT><SPAN style="FONT: 7pt 'Times New Roman'">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </SPAN></SPAN><SPAN lang=EN-US style="COLOR: blue; FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>-2.4273<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>m=4 ,y_2_3<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="COLOR: blue; FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>f =<SPAN style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </SPAN>0.0006<SPAN style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </SPAN>0.9950<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN><o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="COLOR: blue; FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>-6.0302<SPAN style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </SPAN>5.2801<SPAN style="mso-spacerun: yes">&nbsp;&nbsp; </SPAN>-2.8196<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none"><SPAN lang=EN-US style="COLOR: blue; FONT-FAMILY: 'Courier New'; mso-bidi-font-family: 'Times New Roman'"><FONT size=3>&nbsp;<o:p></o:p></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=3><SPAN style="FONT-FAMILY: 仿宋_GB2312; mso-ascii-font-family: 'Times New Roman'">运行后，比较拟合后多项式和原式</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 仿宋_GB2312"><o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=3><SPAN style="FONT-FAMILY: 仿宋_GB2312; mso-ascii-font-family: 'Times New Roman'">的系数，发现三次多项式系数与原</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 仿宋_GB2312"><o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=3><SPAN style="FONT-FAMILY: 仿宋_GB2312; mso-ascii-font-family: 'Times New Roman'">系数比较接近，四次多项式的四次项系数很小。作图后，发现二次多项式与原函数的差别比较大，而三次多项式和四次多项式符合得比较好。</SPAN><SPAN lang=EN-US style="mso-fareast-font-family: 仿宋_GB2312"><o:p></o:p></SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><SPAN lang=EN-US><FONT face="Times New Roman"><FONT size=3>&nbsp;<o:p></o:p></FONT></FONT></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><FONT size=3><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">第</SPAN><SPAN lang=EN-US><FONT face="Times New Roman">6</FONT></SPAN><SPAN style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">题</SPAN></FONT></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 12pt; LINE-HEIGHT: 150%; mso-char-indent-count: 1.0; mso-char-indent-size: 12.0pt"><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">解</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">:<SPAN style="mso-spacerun: yes">&nbsp;&nbsp;&nbsp; </SPAN></FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">分析</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">:</FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">电容器充电的数学模型已经建立。由题目给的方程</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><SPAN style="mso-text-raise: -6.0pt"><v:shape id=_x0000_i1025 style="WIDTH: 140.25pt; HEIGHT: 18pt" type="#_x0000_t75" o:ole=""><FONT face="Times New Roman"> <v:imagedata o:title="" src="file&#58///C:/DOCUME~1/LIZHAO~1/LOCALS~1/Temp/msoclip1/01/clip_image008.wmz"></v:imagedata></FONT></v:shape></SPAN><FONT face="Times New Roman">(</FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">已知</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">V=10)</FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">可见，</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">(t)</FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">与τ成指数变化关系，所以在通过曲线拟合的时候，使用指数曲线</SPAN><SPAN lang=EN-US style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">y</FONT></SPAN><SPAN style="FONT-SIZE: 14pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">＝</SPAN><FONT face="Times New Roman"><SPAN lang=EN-US style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt">a<SUB>1</SUB>e</SPAN><SUP><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">a</SPAN></SUP><SUB><SPAN lang=EN-US style="FONT-SIZE: 9pt; mso-bidi-font-size: 10.0pt">2</SPAN></SUB><SUP><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt">x</SPAN></SUP></FONT><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">(</FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">注：这是一种非线性拟合</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">). </FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">首先进行变量代换</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">(</FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为了程序运行的方便，在程序中用</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">v<SUB>1</SUB></FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">代替</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">v(t)</FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">v<SUB>2</SUB></FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">是拟合后的曲线方程</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><FONT face="Times New Roman">)</FONT></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">：</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-INDENT: 12pt; LINE-HEIGHT: 150%; TEXT-ALIGN: center; mso-char-indent-count: 1.0; mso-char-indent-size: 12.0pt" align=center><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">对</SPAN><SPAN lang=EN-US style="FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt"><SPAN style="mso-text-raise: -6.0pt"><v:shape id=_x0000_i1026 style="WIDTH: 2in; HEIGHT: 18pt" type="#_x0000_t75" o:ole=""><FONT face="Times New Roman"> <v:imagedata o:title="" src="file&#58///C:/DOCUME~1/LIZHAO~1/LOCALS~1/Temp/msoclip1/01/clip_image010.wmz"></v:imagedata></FONT></v:shape></SPAN></SPAN><SPAN style="FONT-SIZE: 12pt; FONT-FAMILY: 宋体; LETTER-SPACING: -1pt; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">变形后取对数，