Krylov Documentation

This directory contains the implemented Krylov solver contracts, numerical validation evidence, and supporting estimator rationale.

Canonical Guides

• Matrix-free GMRES and refinement defines fixed right preconditioning, explicit precision roles, residual stopping and publication.
• Krylov Algorithms defines supported solvers, parameters, scalar behavior, and convergence semantics.
• Solver Defaults records public defaults separately from internal tuning.
• Precision Validation records the compiler, precision, and provider validation matrix.
• Test Matrices describes deterministic Matrix Market fixtures and probe usage.

Numerical Rationale

• Exponential Error Bounds
• Exponential Estimators

Dense Dependencies

Dense BLAS/LAPACK Wrapper Coverage tracks provider and quarantined helper coverage used by projected problems. It is maintained as a linalg inventory rather than part of the Krylov algorithm contract.

Exploratory Policy

• Real Nonsymmetric Arnoldi for iDMRG records exploratory policy for real nonsymmetric transfer problems. It is not a statement that all proposed result forms are implemented.

Source Navigation

• Krylov source map
• Dense linalg source map
• Krylov tests
• Krylov examples