Linear Solvers
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."
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What this skill does
Linear Solvers is a community-contributed Claude Code skill 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 Claude Code skill is built for software engineers, backend developers, full-stack teams, and technical leads building and maintaining production systems. It's part of ClaudSkills (also referred to as Claude Skills or Claude Code Skills) — the open community-curated registry of 153,000+ SKILL.md files for Anthropic's Claude Code agent and the wider Claude ecosystem (Claude API, Claude Agent SDK).
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.
Telegram
📱 Install from your phone or desktop Telegram
Open @claudskills_bot on Telegram, tap Open Desktop App, and the desktop app installs this skill for you. Or share the bot link with a colleague — they get the same one-tap install. Learn more →
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.
Pro
For the full experience including quality scoring and one-click install features for each skill — upgrade to Pro.
Frequently asked questions
How do I install the Linear Solvers Claude Code skill?
Install via the ClaudSkills desktop app (one click) or copy
SKILL.md from the source repository to
~/.claude/skills/linear-solvers/SKILL.md and restart Claude Code. Both flows are detailed at
claudskills.com/install/.
What does the Linear Solvers skill do?
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."
Is this skill free to install?
Yes. ClaudSkills is an open registry — every skill keeps its source repository's license, and manual install via copy is free. ClaudSkills Pro ($9/mo, $79/yr, or $149 one-time) adds one-click install via the desktop app and a multi-signal Quality Score.
When should I use the Linear Solvers skill?
Use Linear Solvers when your Claude Code task falls under the Engineering category — specifically in the performance area. Claude Code auto-discovers installed skills and invokes the right one based on the task description, so you can also ask Claude directly (e.g. "use Linear Solvers" or describe the task and let Claude pick). Browse related skills at
/category/engineering/.
What is a Claude Code skill and how does the Linear Solvers skill fit in?
A Claude Code skill is a
SKILL.md file that lives under
~/.claude/skills/<name>/ and tells the Claude Code CLI agent how to perform a specific task (instructions, prompts, allowed tools). Skills are auto-discovered at session start. Linear Solvers is one of 67,000+ skills indexed in the open ClaudSkills catalog, classified under the Engineering category. Learn more at
/learn/what-is-a-claude-skill/.
Attribution & license
Cite this skill
If you reference this skill in a blog post, paper, or documentation, you can cite it as:
APA
FreedomIntelligence. (2026). Linear Solvers [Claude Code skill]. ClaudSkills. https://claudskills.com/skills/linear-solvers/
BibTeX
@misc{linear-solvers-2026,
author = {FreedomIntelligence},
title = {Linear Solvers [Claude Code skill]},
year = {2026},
publisher = {ClaudSkills},
url = {https://claudskills.com/skills/linear-solvers/}
}Embed this skill
Promote, attribute, or link this skill from your own README, blog post, or documentation. All three snippets are free to use — no sign-up, no API key. More distribution surfaces →
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Security scan
Grade A · scanned 2026-07-18 — free static scan against the OWASP Agentic Skills Top 10.
The scan flagged 1 of 10 categories (execution), including lower-severity patterns. Patterns shown inside code fences are weighted as examples rather than instructions — read the grading methodology for what this does and does not guarantee.
- ✓ Prompt injection
- ✓ Data exfiltration
- ✓ Supply chain
- ✓ Reverse shell
- ✓ Credentials
- ⚠ Execution
- ✓ Filesystem
- ✓ Persistence
- ✓ Obfuscation
- ✓ Network
Show this grade on your repo (click to copy):
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