linear-solvers

What problem does it solve?

This Skill helps you pick and configure linear solvers for Ax = b, covering direct versus iterative methods, diagnosing convergence issues, estimating conditioning, selecting preconditioners, and debugging stagnation in common solvers like GMRES, CG, and BiCGSTAB.

Core Features & Use Cases

• Solver selection: Decide between direct and iterative solvers based on matrix size, sparsity, and structure.
• Convergence diagnostics: Assess stagnation, convergence rate, and residual trends to adjust strategy.
• Preconditioner advice: Recommend appropriate preconditioners (e.g., ILU, IC, AMG) for improved robustness.
• Scaling guidance: Suggest scaling/equilibration steps when conditioning is poor.
• Use Case: You have a large SPD sparse system; this Skill guides you to use CG with AMG/IC preconditioning and to monitor residuals for stagnation.

Quick Start

Run a quick solver recommendation for a symmetric positive definite sparse matrix: python3 scripts/solver_selector.py --symmetric --positive-definite --sparse --size 1000000 --json