scipy.sparse.linalg.minres¶
- scipy.sparse.linalg.minres(A, b, x0=None, shift=0.0, tol=1e-05, maxiter=None, xtype=None, M=None, callback=None, show=False, check=False)[source]¶
Use MINimum RESidual iteration to solve Ax=b
MINRES minimizes norm(A*x - b) for a real symmetric matrix A. Unlike the Conjugate Gradient method, A can be indefinite or singular.
If shift != 0 then the method solves (A - shift*I)x = b
Parameters: A : {sparse matrix, dense matrix, LinearOperator}
The real symmetric N-by-N matrix of the linear system
b : {array, matrix}
Right hand side of the linear system. Has shape (N,) or (N,1).
Returns: x : {array, matrix}
The converged solution.
info : integer
- Provides convergence information:
0 : successful exit >0 : convergence to tolerance not achieved, number of iterations <0 : illegal input or breakdown
Other Parameters: x0 : {array, matrix}
Starting guess for the solution.
tol : float
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.
xtype : {‘f’,’d’,’F’,’D’}
This parameter is deprecated – avoid using it.
The type of the result. If None, then it will be determined from A.dtype.char and b. If A does not have a typecode method then it will compute A.matvec(x0) to get a typecode. To save the extra computation when A does not have a typecode attribute use xtype=0 for the same type as b or use xtype=’f’,’d’,’F’,or ‘D’. This parameter has been superseded by LinearOperator.
Notes
THIS FUNCTION IS EXPERIMENTAL AND SUBJECT TO CHANGE!
References
- Solution of sparse indefinite systems of linear equations,
- C. C. Paige and M. A. Saunders (1975), SIAM J. Numer. Anal. 12(4), pp. 617-629. http://www.stanford.edu/group/SOL/software/minres.html
- This file is a translation of the following MATLAB implementation:
- http://www.stanford.edu/group/SOL/software/minres/matlab/