Linear Solvers

Quality score: 70/100 · Category: Engineering · Sub-category: performance

tool:lineartype:debug

Select and configure linear solvers for Ax=b systems arising in numerical simulations — choose between direct (LU, Cholesky) and iterative (CG, GMRES, BiCGSTAB, MINRES) methods, analyze sparsity patterns and matrix conditioning, recommend preconditioners (AMG, ILU, IC), apply row/column scaling, and diagnose convergence stagnation from residual histories. Use when setting up a linear solve for FEM/FVM assembly, debugging slow or stalled Krylov iterations, choosing a preconditioner for SPD or nonsymmetric systems, or investigating ill-conditioning, even if the user only says "my solver is slow" or "GMRES won't converge."

What this skill does

Linear Solvers is a production-ready Claude Code skill (quality score 70/100) in the performance sub-category. It ships as a SKILL.md file that Claude Code auto-discovers under ~/.claude/skills/linear-solvers/ and loads when your prompt matches the skill's trigger.

When to invoke it: Use when setting up a linear solve for FEM/FVM assembly, debugging slow or stalled Krylov iterations, choosing a preconditioner for SPD or nonsymmetric systems, or investigating ill-conditioning, even if the user only says "my solver is slow" or "GMRES won't converge.

Who uses this skill

The Linear Solvers skill is built for software engineers, backend developers, full-stack teams, and technical leads building and maintaining production systems. It is part of the open ClaudSkills registry, a community-curated catalog of 15,000+ capabilities you can install for Claude Code — the Claude CLI agent.

How to install

Free

Manual install (2 steps)

mkdir -p ~/.claude/skills/linear-solvers
curl -L https://claudskills.com/skills/linear-solvers/SKILL.md \
  -o ~/.claude/skills/linear-solvers/SKILL.md

Or just download SKILL.md directly and drop it into ~/.claude/skills/linear-solvers/. Claude Code auto-discovers it on next session.

Skills live at ~/.claude/skills/linear-solvers/SKILL.md on macOS/Linux, or %USERPROFILE%\.claude\skills\linear-solvers\SKILL.md on Windows. See the full install guide for step-by-step instructions.

Pro

One-click install via the desktop app

The ClaudSkills desktop app installs any skill directly into ~/.claude/skills/ with one click — no terminal required. Pro starts at $9/mo or $149 lifetime.

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