linear-solvers
Select and configure linear solvers for systems Ax=b in dense and sparse problems. Use when choosing direct vs iterative methods, diagnosing convergence issues, estimating conditioning, selecting preconditioners, or debugging stagnation in GMRES/CG/BiCGSTAB.
npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill linear-solvers --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Linear Solvers ## Goal Provide a universal workflow to select a solver, assess conditioning, and diagnose convergence for linear systems arising in numerical simulations. ## Requirements - Python 3.8+ - NumPy, SciPy (for matrix operations) - See individual scripts for dependencies ## Inputs to Gather | Input | Description | Example | |-------|-------------|---------| | Matrix size | Dimension of system | `n = 1000000` | | Sparsity | Fraction of nonzeros | `0.01%` | | Symmetry | Is A = Aᵀ? | `yes` | | Definiteness | Is A positive definite? | `yes (SPD)` | | Conditioning | Estimated condition number | `10⁶` | ## Decision Guidance ### Solver Selection Flowchart ``` Is matrix small (n < 5000) and dense? ├── YES → Use direct solver (LU, Cholesky) └── NO → Is matrix symmetric? ├── YES → Is it positive definite? │ ├── YES → Use CG with AMG/IC preconditioner │ └── NO → Use MINRES └── NO → Is it nearly symmetric? ├── YES → Use BiCGSTAB └── NO → Use GMRES with ILU/AMG ``` ### Quick Reference | Matrix Type | Solver | Preconditioner | |-------------|--------|----------------| | SPD, sparse | CG | AMG, IC | | Symmetric indefinite | MINRES | ILU | | Nonsymmetric | GMRES, BiCGSTAB | ILU, AMG |
- Goal
- Requirements
- Inputs to Gather
- Decision Guidance
- Solver Selection Flowchart
- Quick Reference
- Script Outputs (JSON Fields)
- Workflow
- Conversational Workflow Example
- Pre-Solve Checklist
- CLI Examples
- Error Handling
- Interpretation Guidance
- Convergence Rate
python3 scripts/convergence_diagnostics.py --residuals 1,0.1,0.01,0.005,0.003,0.002,0.002,0.002 --json python3 scripts/preconditioner_advisor.py --matrix-type nonsymmetric --sparse --stagnation --json Analyze sparsity pattern python3 scripts/sparsity_stats.py --matrix A.npy --json Select solver for SPD sparse system python3 scripts/solver_selector.py --symmetric --positive-definite --sparse --size 1000000 --json Get preconditioner recommendation python3 scripts/preconditioner_advisor.py --matrix-type spd --sparse --json Diagnose convergence from residual history python3 scripts/convergence_diagnostics.py --residuals 1,0.2,0.05,0.01 --json
What does the linear-solvers skill do?
Select and configure linear solvers for systems Ax=b in dense and sparse problems. Use when choosing direct vs iterative methods, diagnosing convergence issues, estimating conditioning, selecting preconditioners, or debugging stagnation in GMRES/CG/BiCGSTAB.
How do I install it?
Run `npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill linear-solvers --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From FreedomIntelligence/OpenClaw-Medical-Skills, a repository with 2,909 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.