class trainsum.gmres.GMRES(nsteps=10, subspace=10, eps=1e-08, solver=<trainsum.lstsqsolver.LstsqSolver object>)

GMRES linear solver.

Parameters:
nsteps: int = 10

Number of times the subspace is created and solved

subspace: int = 10

Size of the Arnoldi basis

eps: float = 1e-08

Minimum residual, after which the algorithm is stopped

solver: MatrixLeastSquares = <trainsum.lstsqsolver.LstsqSolver object>

Least squares solver for solving the matrix in the Arnoldi basis

Parameters:

  • A (T)

  • b (T)

Return type:

T

__call__(mat, rhs, guess=None, /)

Solve the linear system with mat being a linear operator and rhs being the right hand side of the equation. The initial guess can be provided, otherwise it will be initialized to zero.

Parameters:

  • mat (Callable[[T], T])

  • rhs (T)

  • guess (T | None)

Return type:

GMRESResult