gko::solver

Iterative and direct linear solvers. Every solver is a LinOp built from a system matrix; iterative solvers also take stopping criteria. Each exposes a typed Factory produced by the build() method. For the high-level taxonomy and how to pick a solver see the Solvers overview concept page.

Krylov: symmetric / SPD systems

• Cg: conjugate gradient.

• Fcg: flexible conjugate gradient (variable preconditioner).

• PipeCg: pipelined CG (overlapped reductions).

• Minres: minimum residual (symmetric indefinite).

Krylov: non-symmetric systems

• Bicg: biconjugate gradient.

• Bicgstab: stabilised biconjugate gradient.

• Cgs: conjugate gradient squared.

• Gmres: generalised minimal residual.

• CbGmres: compressed-basis GMRES (mixed precision).

• Idr: induced dimension reduction.

• Gcr: generalised conjugate residual.

Stationary and miscellaneous

• Ir: iterative refinement / Richardson iteration.

• Chebyshev: Chebyshev iteration.

Triangular substitution

• LowerTrs: lower-triangular solve.

• UpperTrs: upper-triangular solve.

Direct (factorisation-based)

• experimental::solver::Direct: pairs a sparse factorisation with LowerTrs / UpperTrs to act as a LinOp.

Multigrid

• Multigrid: geometric / algebraic multigrid framework.

Singular systems

• Nullspace: orthogonal projector \(I - V V^H\) onto the complement of a nullspace (explicit basis, the constant vector, or both). Pass it as the nullspace / left_nullspace factory parameter of Cg, Fcg, Minres, Gmres or Bicgstab to solve singular systems (minimum-norm or least-squares solution).

• preconditioner::NullspaceProjection: wraps a preconditioner so that its output stays orthogonal to the nullspace.