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Conjugate gradient method of Golub and van Loan - Revision history
2024-03-29T08:25:48Z
Revision history for this page on the wiki
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Peter: Reverted edits by SitelTrlet (Talk) to last version by Tsaad
2008-12-19T12:39:31Z
<p>Reverted edits by <a href="/Wiki/Special:Contributions/SitelTrlet" title="Special:Contributions/SitelTrlet">SitelTrlet</a> (<a href="/W/index.php?title=User_talk:SitelTrlet&action=edit&redlink=1" class="new" title="User talk:SitelTrlet (page does not exist)">Talk</a>) to last version by <a href="/Wiki/User:Tsaad" title="User:Tsaad">Tsaad</a></p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">basbocolobo</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conjugate gradient method ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conjugate gradient method ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Conjugate gradient method could be summarized as follows <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Conjugate gradient method could be summarized as follows <br></div></td></tr>
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Peter
https://cfd-online.com/W/index.php?title=Conjugate_gradient_method_of_Golub_and_van_Loan&diff=9524&oldid=prev
SitelTrlet: laelttrocelt
2008-12-19T09:50:16Z
<p>laelttrocelt</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 09:50, 19 December 2008</td>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">basbocolobo</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conjugate gradient method ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Conjugate gradient method ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Conjugate gradient method could be summarized as follows <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Conjugate gradient method could be summarized as follows <br></div></td></tr>
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SitelTrlet
https://cfd-online.com/W/index.php?title=Conjugate_gradient_method_of_Golub_and_van_Loan&diff=4878&oldid=prev
Tsaad: fixed dot product notation---again!
2005-12-15T20:35:02Z
<p>fixed dot product notation---again!</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: Allocate temerary reals rho_0, rho_1 , alpha, beta <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: Allocate temerary reals rho_0, rho_1 , alpha, beta <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: <br> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: <br> </div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>: r := b - A<math>\<del class="diffchange diffchange-inline">bullet</del></math>x <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>: r := b - A<math>\<ins class="diffchange diffchange-inline">cdot</ins></math>x <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: for i := 1 step 1 until max_itr do</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: for i := 1 step 1 until max_itr do</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:: solve (M<math>\<del class="diffchange diffchange-inline">bullet</del></math>z = r ) <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:: solve (M<math>\<ins class="diffchange diffchange-inline">cdot</ins></math>z = r ) <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:: beta := rho_0 / rho_1 <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:: beta := rho_0 / rho_1 <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:: p := z + beta<math>\<del class="diffchange diffchange-inline">bullet</del></math>p <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:: p := z + beta<math>\<ins class="diffchange diffchange-inline">cdot</ins></math>p <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:: q := A<math>\bullet</math>p <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:: q := A<math>\bullet</math>p <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:: alpha = rho_0 / ( p<math>\<del class="diffchange diffchange-inline">bullet</del></math>q ) <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:: alpha = rho_0 / ( p<math>\<ins class="diffchange diffchange-inline">cdot</ins></math>q ) <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:: x := x + alpha<math>\<del class="diffchange diffchange-inline">bullet</del></math>p <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:: x := x + alpha<math>\<ins class="diffchange diffchange-inline">cdot</ins></math>p <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:: r := r - alpha<math>\<del class="diffchange diffchange-inline">bullet</del></math>q <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:: r := r - alpha<math>\<ins class="diffchange diffchange-inline">cdot</ins></math>q <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:: rho_1 = rho_0 <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>:: rho_1 = rho_0 <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: end (i-loop)</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: end (i-loop)</div></td></tr>
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Tsaad
https://cfd-online.com/W/index.php?title=Conjugate_gradient_method_of_Golub_and_van_Loan&diff=3106&oldid=prev
Zxaar at 06:25, 3 October 2005
2005-10-03T06:25:41Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#'''Richard Barret, Michael Berry, Tony F. Chan, James Demmel, June M. Donato, Jack Dongarra, Victor Eijihout, Roldan Pozo, Charles Romine, Henk Van der Vorst''', "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods"</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#'''Richard Barret, Michael Berry, Tony F. Chan, James Demmel, June M. Donato, Jack Dongarra, Victor Eijihout, Roldan Pozo, Charles Romine, Henk Van der Vorst''', "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods"</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#'''Ferziger, J.H. and Peric, M. 2002'''. <i>Computational Methods for Fluid Dynamics</i>, 3rd rev. ed., Springer-Verlag, Berlin.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#'''Ferziger, J.H. and Peric, M. 2002'''. <i>Computational Methods for Fluid Dynamics</i>, 3rd rev. ed., Springer-Verlag, Berlin.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">----</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><i> Return to [[Numerical methods | Numerical Methods]] </i></ins></div></td></tr>
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Zxaar
https://cfd-online.com/W/index.php?title=Conjugate_gradient_method_of_Golub_and_van_Loan&diff=2160&oldid=prev
Zxaar at 07:50, 15 September 2005
2005-09-15T07:50:17Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#'''Richard Barret, Michael Berry, Tony F. Chan, James Demmel, June M. Donato, Jack Dongarra, Victor Eijihout, Roldan Pozo, Charles Romine, Henk Van der Vorst''', "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods"</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>#'''Richard Barret, Michael Berry, Tony F. Chan, James Demmel, June M. Donato, Jack Dongarra, Victor Eijihout, Roldan Pozo, Charles Romine, Henk Van der Vorst''', "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods"</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>#'''Ferziger, J.H. and Peric, M. 2002'''. <del class="diffchange diffchange-inline">"</del>Computational Methods for Fluid Dynamics<del class="diffchange diffchange-inline">"</del>, 3rd rev. ed., Springer-Verlag, Berlin.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>#'''Ferziger, J.H. and Peric, M. 2002'''. <ins class="diffchange diffchange-inline"><i></ins>Computational Methods for Fluid Dynamics<ins class="diffchange diffchange-inline"></i></ins>, 3rd rev. ed., Springer-Verlag, Berlin.</div></td></tr>
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Zxaar
https://cfd-online.com/W/index.php?title=Conjugate_gradient_method_of_Golub_and_van_Loan&diff=2124&oldid=prev
Zxaar at 00:44, 15 September 2005
2005-09-15T00:44:33Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Reference ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Reference ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>''Ferziger, J.H. and Peric, M. 2002''. "Computational Methods for Fluid Dynamics", 3rd rev. ed., Springer-Verlag, Berlin.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">#'''Richard Barret, Michael Berry, Tony F. Chan, James Demmel, June M. Donato, Jack Dongarra, Victor Eijihout, Roldan Pozo, Charles Romine, Henk Van der Vorst''', "Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods"</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">#'</ins>''Ferziger, J.H. and Peric, M. 2002<ins class="diffchange diffchange-inline">'</ins>''. "Computational Methods for Fluid Dynamics", 3rd rev. ed., Springer-Verlag, Berlin.</div></td></tr>
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Zxaar
https://cfd-online.com/W/index.php?title=Conjugate_gradient_method_of_Golub_and_van_Loan&diff=2052&oldid=prev
Zxaar at 08:15, 14 September 2005
2005-09-14T08:15:37Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Algorithm ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Algorithm ===</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">----</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>Allocate temperary vectors p,z,q <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: </ins>Allocate temperary vectors p,z,q <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>Allocate temerary reals rho_0, rho_1 , alpha, beta <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: </ins>Allocate temerary reals rho_0, rho_1 , alpha, beta <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: <br> </ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>r := b - A<math>\bullet</math>x <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: </ins>r := b - A<math>\bullet</math>x <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>for i := 1 step 1 until max_itr do</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: <br></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>solve (M<math>\bullet</math>z = r ) <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: </ins>for i := 1 step 1 until max_itr do</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>beta := rho_0 / rho_1 <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:: </ins>solve (M<math>\bullet</math>z = r ) <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>p := z + beta<math>\bullet</math>p <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:: </ins>beta := rho_0 / rho_1 <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>q := A<math>\bullet</math>p <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:: </ins>p := z + beta<math>\bullet</math>p <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>alpha = rho_0 / ( p<math>\bullet</math>q ) <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:: </ins>q := A<math>\bullet</math>p <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>x := x + alpha<math>\bullet</math>p <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:: </ins>alpha = rho_0 / ( p<math>\bullet</math>q ) <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>r := r - alpha<math>\bullet</math>q <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:: </ins>x := x + alpha<math>\bullet</math>p <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>rho_1 = rho_0 <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:: </ins>r := r - alpha<math>\bullet</math>q <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>end (i-loop)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:: </ins>rho_1 = rho_0 <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: </ins>end (i-loop)</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>deallocate all temp memory <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: <br></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"> </del>return TRUE <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: </ins>deallocate all temp memory <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">: </ins>return TRUE <br></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">----</ins></div></td></tr>
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Zxaar
https://cfd-online.com/W/index.php?title=Conjugate_gradient_method_of_Golub_and_van_Loan&diff=2020&oldid=prev
Zxaar at 05:34, 14 September 2005
2005-09-14T05:34:44Z
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 05:34, 14 September 2005</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> deallocate all temp memory <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> deallocate all temp memory <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> return TRUE <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> return TRUE <br></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== Reference ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">''Ferziger, J.H. and Peric, M. 2002''. "Computational Methods for Fluid Dynamics", 3rd rev. ed., Springer-Verlag, Berlin.</ins></div></td></tr>
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Zxaar
https://cfd-online.com/W/index.php?title=Conjugate_gradient_method_of_Golub_and_van_Loan&diff=2019&oldid=prev
Zxaar at 05:30, 14 September 2005
2005-09-14T05:30:36Z
<p></p>
<p><b>New page</b></p><div>== Conjugate gradient method ==<br />
Conjugate gradient method could be summarized as follows <br><br />
<br />
=== System of equation ===<br />
For the given system of equation <br> Ax = b ;<br> <br />
b = source vector <br><br />
x = solution variable for which we seek the solution <br><br />
A = coefficient matrix <br><br />
<br />
M = the precondioning matrix constructued by matrix A <br><br />
<br />
<br />
=== Algorithm ===<br />
<br />
Allocate temperary vectors p,z,q <br><br />
Allocate temerary reals rho_0, rho_1 , alpha, beta <br><br />
<br />
r := b - A<math>\bullet</math>x <br><br />
for i := 1 step 1 until max_itr do<br />
solve (M<math>\bullet</math>z = r ) <br><br />
beta := rho_0 / rho_1 <br><br />
p := z + beta<math>\bullet</math>p <br><br />
q := A<math>\bullet</math>p <br><br />
alpha = rho_0 / ( p<math>\bullet</math>q ) <br><br />
x := x + alpha<math>\bullet</math>p <br><br />
r := r - alpha<math>\bullet</math>q <br><br />
rho_1 = rho_0 <br><br />
end (i-loop)<br />
<br />
deallocate all temp memory <br><br />
return TRUE <br></div>
Zxaar