Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill numerical-analysis-and-computationgit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/numerical-analysis-and-computation)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/numerical-analysis-and-computation"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/numerical-analysis-and-computation/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/numerical-analysis-and-computation"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/numerical-analysis-and-computation.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00062 | $0.00539 |
| Opus 5.5 | $0.00025 | $0.00216 |
| Sonnet 5.5 | $0.00012 | $0.00108 |
| Haiku 4.5 | $0.00006 | $0.00054 |
Grade A, and why
numerical-analysis-and-computation scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
What it actually says
Numerical Analysis & Computation
Floating point
IEEE 754 double: 53-bit mantissa, machine epsilon 2.2e-16; catastrophic cancellation (rewrite sqrt(x+1) - sqrt(x) = 1/(sqrt(x+1) + sqrt(x))); overflow/underflow; summation with Kahan; relative vs absolute error; condition number of a problem vs stability of an algorithm.
Root finding
Bisection (linear, guaranteed), Newton (quadratic, needs derivative), secant (order 1.618), Brent (robust default), fixed-point iteration (converges if |g'| < 1), polynomial roots via companion matrix eigenvalues.
Interpolation & approximation
Lagrange/Newton interpolation (Runge phenomenon -> use Chebyshev nodes), splines (cubic), least squares, minimax (Remez), Pade approximants, Chebyshev series.
Integration & differentiation
Trapezoid O(h^2), Simpson O(h^4), Gauss-Legendre (exact to degree 2n-1), Romberg, adaptive quadrature, Monte Carlo (1/sqrt(N)) and quasi-MC for high dimensions; finite differences (central O(h^2); choose h ~ eps^{1/3}), automatic differentiation (exact derivatives to machine precision).
Linear algebra numerics
LU with partial pivoting, Cholesky, QR (Householder), SVD; iterative: Jacobi, Gauss-Seidel, conjugate gradient, GMRES; eigen: power iteration, QR algorithm, Lanczos; sparse storage; preconditioning.
Differential equations
Euler, Heun, RK4, adaptive RK45, multistep, stiff solvers (BDF, implicit RK), symplectic integrators; global error ~ h^p; stability regions; PDE: FD/FE/FV, CFL.
FFT & signal
FFT O(n log n); convolution via FFT; spectral methods for smooth periodic problems.
Workflow
Choose the method by smoothness and size, estimate error, run convergence tests (halve h), compare against a known solution. Scripts: scripts/numerics.py (Brent/Newton, Gauss quadrature, Chebyshev interpolation, convergence-order estimator).
What ships with it
2 files beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 31 lines · 62 tokens per session scan A 908cf2ab7fb6
numerical-analysis-and-computation is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 62 tokens to every session and 539 once invoked, about $0.0002 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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