bicgstab
Solve a system of linear equations with the biconjugate gradient stabilized method.
Syntax
x = bicgstab(A,b)
x = bicgstab(A,b,rtol)
x = bicgstab(A,b,rtol,maxit)
x = bicgstab(A,b,rtol,maxit,M1)
x = bicgstab(A,b,rtol,maxit,M1,M2)
x = bicgstab(A,b,rtol,maxit,M1,M2,x0)
[x, iflag, relres, iter, resvec] = bicgstab(...)
Inputs
- A
- The left-hand side matrix, or a function name or handle to generate A*x.
- b
- The right-hand side vector.
- rtol
- The relative convergerce tolerance (default: 1.0e-6).
- maxit
- The maximum number of iterations (default: min(size(b, 1), 20)).
- M1
- The left preconditioner matrix, or a function name or handle to generate M1\x. (default: none or [])
- M2
- The right preconditioner matrix, or a function name or handle to generate M2\x. (default: none or [])
- x0
- The initial estimate of the solution (default: zeroes(length(b),1)).
Outputs
- x
- The solution vector.
- iflag
- The termination status.
- iflag = 0:
- The algorithm converged within the allowed tolerance and number of iterations.
- iflag = 1:
- The algorithm completed the allowed iterations without converging.
- iflag = 2:
- A preconditioner matrix was singular.
- iflag = 3:
- The algorithm converged, but not at a solution due to stagnation.
- iflag = 4:
- The algorithm stopped prematurely because it could not determine a descent direction.
- relres
- The magnitude of the residual relative to norm(b).
- iter
- The number of iterations performed. If convergence occurs half way through an iteration it is recorded as such.
- resvec
- The residual vector.
Example
Case using a function handle for A and a left preconditioner.
A = [3, 1, 0; 0, 5, 6; -2, 0, 4];
b = [13; 14; -10];
tol = 0.0001;
max_it = 5;
M1 = diag(diag(A));
M2 = [];
x0 = [];
Ahandle = @(x) A * x;
[x, iflag, relres, iter, resvec] = bicgstab(Ahandle, b, tol, max_it, M1, M2, x0)x = [Matrix] 3 x 1
3.00000
4.00000
-1.00000
iflag = 0
relres = 1.30675106e-16
iter = 2.5
resvec = [Matrix] 6 x 1
2.15639e+01
2.10064e+01
6.74333e+00
1.84478e-01
1.35884e-01
2.81786e-15