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linear-solvers

Maintainer FreedomIntelligence · Last updated April 1, 2026

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.

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Original source

FreedomIntelligence/OpenClaw-Medical-Skills

https://github.com/FreedomIntelligence/OpenClaw-Medical-Skills/tree/main/skills/linear-solvers

Maintainer: FreedomIntelligence
License: MIT
Last updated: April 1, 2026

Skill Snapshot

Key Details From SKILL.md

2 min

Key Notes

Provide a universal workflow to select a solver, assess conditioning, and diagnose convergence for linear systems arising in numerical simulations.
python3 scripts/sparsity_stats.py --matrix A.npy --json.

Source Doc

Excerpt From SKILL.md

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`

Script Outputs (JSON Fields)

Script	Key Outputs
`scripts/solver_selector.py`	`recommended`, `alternatives`, `notes`
`scripts/convergence_diagnostics.py`	`rate`, `stagnation`, `recommended_action`
`scripts/sparsity_stats.py`	`nnz`, `density`, `bandwidth`, `symmetry`
`scripts/preconditioner_advisor.py`	`suggested`, `notes`
`scripts/scaling_equilibration.py`	`row_scale`, `col_scale`, `notes`
`scripts/residual_norms.py`	`residual_norms`, `relative_norms`, `converged`

Use cases

Use when choosing direct vs iterative methods, diagnosing convergence issues, estimating conditioning, selecting preconditioners, or debugging stagnation in GMRES/CG/BiCGSTAB.

Not for

Do not rely on this catalog entry alone for installation or maintenance details.

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