nonlinear-solvers
Select and configure nonlinear solvers for f(x)=0 or min F(x). Use for Newton methods, quasi-Newton (BFGS, L-BFGS), Broyden, Anderson acceleration, diagnosing convergence issues, choosing line search vs trust region, and analyzing Jacobian quality.
npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill nonlinear-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.
# Nonlinear Solvers ## Goal Provide a universal workflow to select a nonlinear solver, configure globalization strategies, and diagnose convergence for root-finding, optimization, and least-squares problems. ## Requirements - Python 3.8+ - NumPy (for Jacobian diagnostics) - SciPy (optional, for advanced analysis) ## Inputs to Gather | Input | Description | Example | |-------|-------------|---------| | Problem type | Root-finding, optimization, least-squares | `root-finding` | | Problem size | Number of unknowns | `n = 10000` | | Jacobian availability | Analytic, finite-diff, unavailable | `analytic` | | Jacobian cost | Cheap or expensive to compute | `expensive` | | Constraints | None, bounds, equality, inequality | `none` | | Smoothness | Is objective/residual smooth? | `yes` | | Residual history | Sequence of residual norms | `1,0.1,0.01,...` | ## Decision Guidance ### Solver Selection Flowchart ``` Is Jacobian available and cheap? ├── YES → Problem size? │ ├── Small (n < 1000) → Newton (full) │ └── Large (n ≥ 1000) → Newton-Krylov └── NO → Is objective smooth? ├── YES → Memory limited? │ ├── YES → L-BFGS or Broyden │ └── NO → BFGS └── NO → Anderson acceleration or Picard ``` ###
- 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 Type
python3 scripts/convergence_analyzer.py --residuals 1,0.8,0.6,0.5,0.4,0.3,0.2,0.15,0.12,0.1 --json python3 scripts/globalization_advisor.py --problem-type root-finding --jacobian-quality ill-conditioned --previous-failures 0 --json Select solver for large unconstrained optimization python3 scripts/solver_selector.py --size 50000 --smooth --memory-limited --json Analyze convergence from residual history python3 scripts/convergence_analyzer.py --residuals 1,0.1,0.01,0.001,0.0001 --tolerance 1e-6 --json Diagnose Jacobian quality python3 scripts/jacobian_diagnostics.py --matrix jacobian.txt --json Get globalization recommendation python3 scripts/globalization_advisor.py --problem-type optimization --jacobian-quality good --json
What does the nonlinear-solvers skill do?
Select and configure nonlinear solvers for f(x)=0 or min F(x). Use for Newton methods, quasi-Newton (BFGS, L-BFGS), Broyden, Anderson acceleration, diagnosing convergence issues, choosing line search vs trust region, and analyzing Jacobian quality.
How do I install it?
Run `npx skills add FreedomIntelligence/OpenClaw-Medical-Skills --skill nonlinear-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.