3. Solvers
A solver is a function that attempts to solve the equation A x = b.
3.1. Preconditioned Conjugate Gradient Solver
TBD
3.2. Scipy solvers
Operators implement the scipy.sparse.linalg.LinearOperator interface,
so the following solvers are useable as-is, as long as the operator has
explicit input and output shapes.
bicg |
Use BIConjugate Gradient iteration |
bicgstab |
Use BIConjugate Gradient STABilized iteration |
cg |
Use Conjugate Gradient iteration |
cgs |
Use Conjugate Gradient Squared iteration |
gmres |
Use Generalized Minimal RESidual iteration |
lgmres |
Solve a matrix equation using the LGMRES algorithm |
minres |
Use MINimum RESidual iteration |
qmr |
Use Quasi-Minimal Residual iteration |
Since an Operator is callable, it can also readily be used by the
minimisers in scipy.optimize, although the (soon-to-disappear) lack of
an implementation of norms as an Operator makes these solvers not so
useful.
Note that none of these solvers handle MPI-distributed unknowns.