Module preconditioned 

Preconditioned iterative solvers: PCG and PGMRES(m).

Provides preconditioned variants of the Conjugate Gradient and GMRES(m) solvers. A preconditioner approximates M^{-1} to accelerate convergence by reducing the condition number of the effective system.

Algorithm — Preconditioned CG (PCG)

Standard CG with a preconditioner M applied to the residual:

1. r = b - A*x; z = M^{-1}*r; p = z; rz_old = r^T * z
2. For each iteration: a. Ap = A * p b. alpha = rz_old / (p^T * Ap) c. x += alpha * p d. r -= alpha * Ap e. z = M^{-1} * r f. rz_new = r^T * z g. If ||r|| < tol * ||b||: converged h. beta = rz_new / rz_old i. p = z + beta * p j. rz_old = rz_new

Algorithm — Preconditioned GMRES(m) (Left-preconditioned)

Left-preconditioned GMRES builds the Krylov space from M^{-1}*A instead of A, solving the preconditioned system M^{-1} A x = M^{-1} b.

Structs

IdentityPreconditioner

Identity preconditioner (no preconditioning).

IterativeSolverResult

Result from a preconditioned iterative solver.

JacobiPreconditioner

Jacobi (diagonal) preconditioner.

PcgConfig

Configuration for the Preconditioned Conjugate Gradient solver.

PgmresConfig

Configuration for the Preconditioned GMRES(m) solver.

Traits

Preconditioner

Preconditioner trait for iterative solvers.

Functions

preconditioned_cg

Solves A * x = b using the Preconditioned Conjugate Gradient method.

preconditioned_gmres

Solves A * x = b using left-preconditioned GMRES(m) with restart.