Biconjugate gradient method

(Difference between revisions)

Revision as of 08:02, 14 September 2005

Biconjugate gradient method could be summarized as follows

For the given system of equation
Ax = b ;
b = source vector
x = solution variable for which we seek the solution
A = coefficient matrix

M = the precondioning matrix constructued by matrix A

 Has to be added very soon.

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 === Algorithm ===
+   Has to be added very soon.
-   Allocate temperary vectors p, phat, s, shat, t, v, rtilde  <br>
-  Allocate temerary reals rho_1, rho_2 , alpha, beta, omega <br>
-  r := b - A<math>\bullet</math>x <br>
-  rtilde = r <br>
-  for i := 1 step 1 until max_itr do
-      rho_1 = rtilde<math>\bullet</math>r <br>
-      if i = 1 then p := r else <br>
-         beta = (rho_1/rho_2) * (alpha/omega)<br>
-         p = r + beta * (p - omega * v) <br>
-      end if <br>
-      solve (M<math>\bullet</math>phat  = p ) <br>
-      v = A<math>\bullet</math>phat <br>
-      alpha = rho_1 / (rtilde<math>\bullet</math>v) <br>
-      s = r - alpha * v <br>
-      solve (M<math>\bullet</math>shat = s ) <br>
-      t = A * shat;
-      omega = (t<math>\bullet</math>s) / (t<math>\bullet</math>t) <br>
-      x = x + alpha * phat + omega * shat <br>
-      r = s - omega * t <br>
-      rho_2 = rho_1 <br>
-  end (i-loop)
-  deallocate all temp memory <br>
-  return TRUE <br>