scipy tutorial - Baustatik-Info-Server

SciPy Reference Guide, Release 0.8.dev
gmres(A, b, x0=None, tol=1.0000000000000001e-05, restrt=20, maxiter=None, xtype=None, M=None, callback=None)
Use Generalized Minimal RESidual iteration to solve A x = b
See Also:
Parameters
A : {sparse matrix, dense matrix, LinearOperator}
LinearOperator
The N-by-N matrix of the linear system.
b : {array, matrix}
Right hand side of the linear system. Has shape (N,) or (N,1).
lgmres(A, b, x0=None, tol=1.0000000000000001e-05, maxiter=1000, M=None, callback=None, inner_m=30,
outer_k=3, outer_v=None, store_outer_Av=True)
Solve a matrix equation using the LGMRES algorithm.
The LGMRES algorithm [BJM] [BPh] is designed to avoid some problems in the convergence in restarted
GMRES, and often converges in fewer iterations.
Parameters
A : {sparse matrix, dense matrix, LinearOperator}
The N-by-N matrix of the linear system.
b : {array, matrix}
Right hand side of the linear system. Has shape (N,) or (N,1).
x0 : {array, matrix}
tol : float
Starting guess for the solution.
Tolerance to achieve. The algorithm terminates when either the relative or the absolute
residual is below tol.
maxiter : integer
Maximum number of iterations. Iteration will stop after maxiter steps even if the
specified tolerance has not been achieved.
M : {sparse matrix, dense matrix, LinearOperator}
Preconditioner for A. The preconditioner should approximate the inverse of A. Effective
preconditioning dramatically improves the rate of convergence, which implies
that fewer iterations are needed to reach a given error tolerance.
callback : function
User-supplied function to call after each iteration. It is called as callback(xk), where
xk is the current solution vector.
Returns
x : array or matrix
The converged solution.
info : integer
396 Chapter 3. Reference