Navigation

Operators and Keywords

Function List:

C++ API

: x = bicgstab (A, b, rtol, maxit, M1, M2, x0)
: x = bicgstab (A, b, rtol, maxit, P)
: [x, flag, relres, iter, resvec] = bicgstab (A, b, …)

Solve A x = b using the stabilizied Bi-conjugate gradient iterative method.

  • - rtol is the relative tolerance, if not given or set to [] the default value 1e-6 is used.
  • - maxit the maximum number of outer iterations, if not given or set to [] the default value min (20, numel (b)) is used.
  • - x0 the initial guess, if not given or set to [] the default value zeros (size (b)) is used.

A can be passed as a matrix or as a function handle or inline function f such that f(x) = A*x.

The preconditioner P is given as P = M1 * M2. Both M1 and M2 can be passed as a matrix or as a function handle or inline function g such that g(x) = M1 \ x or g(x) = M2 \ x.

If called with more than one output parameter

  • - flag indicates the exit status:
    • - 0: iteration converged to the within the chosen tolerance
    • - 1: the maximum number of iterations was reached before convergence
    • - 3: the algorithm reached stagnation

    (the value 2 is unused but skipped for compatibility).

  • - relres is the final value of the relative residual.
  • - iter is the number of iterations performed.
  • - resvec is a vector containing the relative residual at each iteration.

See also: bicg, cgs, gmres, pcg, qmr.

Demonstration 1

The following code

 % Solve system of A*x=b
 A = [5 -1 3;-1 2 -2;3 -2 3];
 b = [7;-1;4];
 [x, flag, relres, iter, resvec] = bicgstab (A, b)

Produces the following output

x =

   1.00000
   1.00000
   1.00000

flag = 0
relres =    7.1911e-15
iter =  3
resvec =

   1.0000e+00
   9.6448e-02
   4.0220e-03
   7.1911e-15

Package: octave