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style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">内建函数</SPAN><SPAN
lang=EN-US> humps</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，我们不须要知道这个方程式的形态为何，不过我们可以将它划出来，再找出根的位置。求根方式如下：</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> x=linspace(-2,3);<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> y=humps(x);<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> plot(x,y), grid % </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">由图中可看出在</SPAN><SPAN
lang=EN-US>0</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">和</SPAN><SPAN
lang=EN-US>1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">附近有二个根</SPAN><SPAN
lang=EN-US> </SPAN></P>
<P class=MsoNormal><!--[if gte vml 1]><V:SHAPETYPE id=_x0000_t75 stroked="f"
filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75"
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o:allowincell="f" type="#_x0000_t75"><V:IMAGEDATA o:title=""
src="./MATLAB入门教程.files/image001.emz" /></V:SHAPE><![endif]--><![if !vml]>
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<td><img width=284 height=213 src="matlab/image002.gif" v:shapes="_x0000_s1063"></td>
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lang=EN-US><![if !supportEmptyParas]><![endif]><O:P></O:P></SPAN>
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<P class=MsoNormal><SPAN
lang=EN-US><![if !supportEmptyParas]><![endif]><O:P></O:P></SPAN></P>
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lang=EN-US><![if !supportEmptyParas]><![endif]><O:P></O:P></SPAN></P>
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lang=EN-US><![if !supportEmptyParas]><![endif]><O:P></O:P></SPAN></P><BR
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<P class=MsoNormal><SPAN lang=EN-US><SPAN style="mso-spacerun: yes">
</SPAN></SPAN></P>
<P class=MsoNormal><SPAN
lang=EN-US><![if !supportEmptyParas]><![endif]> <O:P></O:P></SPAN><SPAN
lang=EN-US>>> r=fzero('humps',1.2)<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>r = 1.2995<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">例三、方程式为</SPAN><SPAN
lang=EN-US>y=x.^3-2*x-5<SPAN style="mso-spacerun: yes">
</SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">这个方程式其实是个多项式，我们说明除了用</SPAN><SPAN
lang=EN-US> roots </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">函数找出它的根外，也可以用这节介绍的方法求根，注意二者的解法及结果有所不同。求根方式如下：</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>% m-function, f_1.m<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>function y=f_1(x) % </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">定义</SPAN><SPAN
lang=EN-US> f_1.m </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">函数</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>y=x.^3-2*x-5;<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> x=linspace(-2,3);<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> y=f_1(x);<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> plot(x,y), grid % </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">由图中可看出在</SPAN><SPAN
lang=EN-US>2</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">和</SPAN><SPAN
lang=EN-US>-1</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">附近有二个根</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><![if !supportEmptyParas]><![endif]>
<SPAN style="mso-spacerun: yes"><IMG height=213 src="matlab2.files/image004.gif"
width=384 align=left v:shapes="_x0000_s1064"></SPAN><O:P></O:P></SPAN></P>
<P class=MsoNormal><SPAN
lang=EN-US><![if !supportEmptyParas]><![endif]><O:P></O:P></SPAN></P>
<P class=MsoNormal><SPAN
lang=EN-US><![if !supportEmptyParas]><![endif]><O:P></O:P></SPAN></P>
<P class=MsoNormal><SPAN
lang=EN-US><![if !supportEmptyParas]><![endif]><O:P></O:P></SPAN></P>
<P class=MsoNormal><!--[if gte vml 1]><V:SHAPE id=_x0000_s1064
style="MARGIN-TOP: -7.8pt; Z-INDEX: 32; LEFT: 0px; MARGIN-LEFT: 27pt; WIDTH: 4in; POSITION: absolute; HEIGHT: 159.8pt; TEXT-ALIGN: left; mso-position-horizontal-relative: text; mso-position-vertical-relative: text"
o:allowincell="f" type="#_x0000_t75"><V:IMAGEDATA o:title=""
src="./MATLAB入门教程.files/image003.emz" /></V:SHAPE><![endif]--><![if !vml]><![endif]><SPAN lang=EN-US><![if !supportEmptyParas]><![endif]><O:P></O:P></SPAN></P><BR
style="mso-ignore: vglayout" clear=all>
<P class=MsoNormal><SPAN lang=EN-US>>> r=fzero('f_1',2); % </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">决定在</SPAN><SPAN
lang=EN-US>2</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">附近的根</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>r = 2.0946<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> p=[1 0 -2 -5]<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> r=roots(p) % </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">以求解多项式根方式验证</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>r =<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>2.0946<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>-1.0473 + 1.1359i <SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>-1.0473 - 1.1359i<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt"><O:P></O:P></SPAN></B></P>
<P class=MsoNormal><B style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt">2</SPAN></B><B
style="mso-bidi-font-weight: normal"><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></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt">5</SPAN></B><B
style="mso-bidi-font-weight: normal"><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'">线性代数方程（组）求解</SPAN></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt"><O:P></O:P></SPAN></B></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">我们习惯将上组方程式以矩阵方式表示如下</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN>AX=B<SPAN
style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">其中</SPAN><SPAN
lang=EN-US> A </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为等式左边各方程式的系数项，</SPAN><SPAN
lang=EN-US>X </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为欲求解的未知项，</SPAN><SPAN
lang=EN-US>B </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">代表等式右边之已知项</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">要解上述的联立方程式，我们可以利用矩阵左除</SPAN><SPAN
lang=EN-US> \ </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">做运算，即是</SPAN><SPAN
lang=EN-US> X=A\B</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">如果将原方程式改写成</SPAN><SPAN
lang=EN-US> XA=B<SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">其中</SPAN><SPAN
lang=EN-US> A </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为等式左边各方程式的系数项，</SPAN><SPAN
lang=EN-US>X </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">为欲求解的未知项，</SPAN><SPAN
lang=EN-US>B </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">代表等式右边之已知项</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">注意上式的</SPAN><SPAN
lang=EN-US> X, B </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">已改写成列向量，</SPAN><SPAN
lang=EN-US>A</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">其实是前一个方程式中</SPAN><SPAN
lang=EN-US> A </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">的转置矩阵。上式的</SPAN><SPAN
lang=EN-US> X </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">可以矩阵右除</SPAN><SPAN
lang=EN-US> / </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">求解，即是</SPAN><SPAN
lang=EN-US> X=B/A</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">若以反矩阵运算求解</SPAN><SPAN
lang=EN-US> AX=B, X=B</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，即是</SPAN><SPAN
lang=EN-US> X=inv(A)*B</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，或是改写成</SPAN><SPAN
lang=EN-US> XA=B, X=B</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">，即是</SPAN><SPAN
lang=EN-US>X=B*inv(A)</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">。</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US><SPAN
style="mso-spacerun: yes"> </SPAN></SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">我们直接以下面的例子来说明这三个运算的用法：</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> A=[3 2 -1; -1 3 2; 1 -1 -1]; %
</SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">将等式的左边系数键入</SPAN><SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN></SPAN></P>
<P class=MsoNormal><SPAN lang=EN-US>>> B=[10 5 -1]'; % </SPAN><SPAN
style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'">将等式右边之已知项键入，</SPAN><SPAN
lang=EN-US>B</SPAN><SPAN
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