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Operators and Keywords

Function List:

C++ API

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

Solve A x = b using the 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, "notransp") = A*x and f(x, "transp") = 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, "notransp") = M1 \ x or g(x, "notransp") = M2 \ x and g(x, "transp") = M1' \ x or g(x, "transp") = 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: bicgstab, cgs, gmres, pcg, qmr.

Package: octave