[分享]共轭斜量法matlab程序
<P >共轭斜量法数学表达式：<p></p></P><P > <v:shapetype><FONT face="Times New Roman"> <v:stroke joinstyle="miter"></v:stroke><v:formulas><v:f eqn="if lineDrawn pixelLineWidth 0"></v:f><v:f eqn="sum @0 1 0"></v:f><v:f eqn="sum 0 0 @1"></v:f><v:f eqn="prod @2 1 2"></v:f><v:f eqn="prod @3 21600 pixelWidth"></v:f><v:f eqn="prod @3 21600 pixelHeight"></v:f><v:f eqn="sum @0 0 1"></v:f><v:f eqn="prod @6 1 2"></v:f><v:f eqn="prod @7 21600 pixelWidth"></v:f><v:f eqn="sum @8 21600 0"></v:f><v:f eqn="prod @7 21600 pixelHeight"></v:f><v:f eqn="sum @10 21600 0"></v:f></v:formulas><v:path connecttype="rect" gradientshapeok="t" extrusionok="f"></v:path><lock aspectratio="t" v:ext="edit"></lock></FONT></v:shapetype><v:shape><v:imagedata></v:imagedata></v:shape>任给初始向量<FONT face="Times New Roman">x<SUP>(0)</SUP>,<p></p></FONT></P>
<P ><FONT face="Times New Roman">r<SUP>(0)</SUP>=b-Ax<SUP>(0)</SUP>,p<SUP>(0)</SUP>=r<SUP>(0)</SUP><p></p></FONT></P>
<P >α<FONT face="Times New Roman"><SUB>k</SUB>=(r<SUP>(k)</SUP>,r<SUP>(k)</SUP>)/(AP<SUP>(k)</SUP>,P<SUP>(k)</SUP>) x<SUP>(k+1)</SUP>=x<SUP>(k)</SUP>+</FONT>α<FONT face="Times New Roman"><SUB>k</SUB>P<SUP>(k)</SUP><p></p></FONT></P>
<P ><FONT face="Times New Roman">r<SUP>(k+1)</SUP>=r<SUP>(k)</SUP>-</FONT>α<FONT face="Times New Roman"><SUB>k</SUB>AP<SUP>(k)</SUP> </FONT>β<FONT face="Times New Roman"><SUB>k</SUB>=(r<SUP>(k+1)</SUP>,r<SUP>(k+1)</SUP>)/(r<SUP>(k)</SUP>,r<SUP>(k)</SUP>)<p></p></FONT></P>
<P ><FONT face="Times New Roman">P<SUP>(k+1)</SUP>=r<SUP>(k+1)</SUP>+</FONT>β<FONT face="Times New Roman"><SUB>k</SUB>P<SUP>(k)</SUP> (k=0,1,2,…..)<p></p></FONT></P>
<P ><FONT face="Times New Roman">%%matlab</FONT>程序<p></p></P>
<P ><FONT face="Times New Roman">%%</FONT>共轭斜量法，程序中变量<FONT face="Times New Roman">alpha</FONT>是α<SUB><FONT face="Times New Roman">k</FONT></SUB>，<FONT face="Times New Roman">beta</FONT>是β<SUB><FONT face="Times New Roman">k<p></p></FONT></SUB></P>
<P ><FONT face="Times New Roman">%%x</FONT>为返回值，<FONT face="Times New Roman">a</FONT>为系数矩阵<FONT face="Times New Roman">b</FONT>列向量</P>
<P ><FONT face="Times New Roman">%%</FONT>函数中添加了计时函数<FONT face="Times New Roman">tic,toc</FONT>也可以不要</P>
<P ><FONT face="Times New Roman">%%</FONT>最多迭代次数为<FONT face="Times New Roman">50</FONT>次</P>
<P ><FONT face="Times New Roman">function x=cg(a,b)</FONT></P>
<P ><FONT face="Times New Roman">=size(b);%</FONT>判断输入的<FONT face="Times New Roman">b</FONT>是行向量还是列向量，如果是行向量，转化成列向量</P>
<P ><FONT face="Times New Roman">if m<n</FONT></P>
<P ><FONT face="Times New Roman"> b=b';</FONT></P>
<P ><FONT face="Times New Roman">end</FONT></P>
<P ><FONT face="Times New Roman">x=zeros(length(a),1);%</FONT>初始迭代值</P>
<P ><FONT face="Times New Roman">tic%</FONT>迭代开计时</P>
<P ><FONT face="Times New Roman">r0=b-a*x;</FONT></P>
<P ><FONT face="Times New Roman">p=r0;</FONT></P>
<P ><FONT face="Times New Roman">r=r0;</FONT></P>
<P ><FONT face="Times New Roman">alpha=dot(r0,r0)/dot(a*p,p);</FONT></P>
<P ><FONT face="Times New Roman">for k=1:50%</FONT>设置最大迭代次数</P>
<P ><FONT face="Times New Roman">x=x+alpha*p;</FONT></P>
<P ><FONT face="Times New Roman">r=r-alpha*a*p;</FONT></P>
<P ><FONT face="Times New Roman">if dot(r,r)<0.0001</FONT></P>
<P ><FONT face="Times New Roman"> fprintf('</FONT>迭代误差为<FONT face="Times New Roman">:%e\n',dot(r,r));</FONT></P>
<P ><FONT face="Times New Roman"> fprintf('</FONT>迭代次数为<FONT face="Times New Roman">:%g\n',k);</FONT></P>
<P ><FONT face="Times New Roman"> t=toc;</FONT></P>
<P ><FONT face="Times New Roman"> fprintf('</FONT>所用时间为<FONT face="Times New Roman">:%g\n',t);</FONT></P>
<P ><FONT face="Times New Roman"> break;</FONT></P>
<P ><FONT face="Times New Roman">end</FONT></P>
<P ><FONT face="Times New Roman">beta=dot(r,r)/dot(r0,r0);</FONT></P>
<P ><FONT face="Times New Roman">p=r+beta*p;</FONT></P>
<P ><FONT face="Times New Roman">alpha=dot(r,r)/dot(a*p,p);</FONT></P>
<P ><FONT face="Times New Roman">r0=r;</FONT></P>
<P ><FONT face="Times New Roman">if k>49%</FONT>超过最大次数，显示警告信息</P>
<P ><FONT face="Times New Roman"> disp('</FONT>已超过最大迭代次数<FONT face="Times New Roman">');</FONT></P>
<P ><FONT face="Times New Roman"> t=toc;</FONT></P>
<P ><FONT face="Times New Roman"> fprintf('</FONT>所用时间为<FONT face="Times New Roman">:%g\n',t);</FONT></P>
<P ><FONT face="Times New Roman"> break;</FONT></P>
<P ><FONT face="Times New Roman">end</FONT></P>
<P ><FONT face="Times New Roman">end</FONT></P>
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