Skill

role-algorithms:numerical-methods

Implements numerical methods — floating-point arithmetic (IEEE 754, Kahan summation, catastrophic cancellation), matrix operations (LU/QR/SVD decomposition, sparse formats), root finding (Newton-Raphson, Brent's method), numerical integration (Simpson, Gaussian quadrature, adaptive), FFT/NTT, and cryptographic foundations (SHA-256, AES-GCM, safe implementation patterns). Use when implementing numerical computation, signal processing, matrix algebra, or cryptographic primitives.

Install

npx claudepluginhub rnavarych/alpha-engineer --plugin role-algorithms

Tool Access

This skill is limited to using the following tools:

ReadGrepGlobBash

Preview

- Diagnosing floating-point precision issues (cancellation, accumulation error, overflow)

Supporting Assets

references/cryptographic-foundations.mdreferences/floating-point-and-matrix.mdreferences/root-finding-and-integration.md

SKILL.md

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Stats

Parent Repo Stars9

Parent Repo Forks0

Last CommitMar 3, 2026

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role-algorithms:numerical-methods

When to use

Diagnosing floating-point precision issues (cancellation, accumulation error, overflow)

Choosing between LU, QR, or SVD decomposition for a linear algebra problem

Implementing root-finding when an analytical solution does not exist

Selecting a numerical integration method based on smoothness and accuracy requirements

Using FFT for polynomial multiplication, convolution, or signal analysis

Reviewing cryptographic primitive usage for correctness and safety

Core principles

Never compare floats with == — always use absolute or relative epsilon; this is not optional

Partial pivoting is not optional in Gaussian elimination — skipping it breaks numerical stability

SVD is the Swiss Army knife — when LU and QR fail or when rank matters, SVD solves it

Brent's method is the default root finder — combines guaranteed convergence with superlinear speed

Never implement your own crypto — use libsodium, OpenSSL, or Web Crypto API; rolling your own is a security incident waiting to happen

Reference Files

references/floating-point-and-matrix.md — IEEE 754 pitfalls, Kahan summation, precision type selection, Gaussian elimination with pivoting, LU/QR/SVD decompositions, sparse matrix formats (COO/CSR/CSC)

references/root-finding-and-integration.md — bisection, Newton-Raphson, secant, Brent's method, trapezoidal/Simpson's/Gaussian quadrature, adaptive integration, Cooley-Tukey FFT, NTT for exact polynomial multiplication

references/cryptographic-foundations.md — secure hash functions (SHA-256, BLAKE3), HMAC, AES-256-GCM, ChaCha20-Poly1305, key derivation (Argon2, bcrypt), RSA/ECDSA/ECDH, timing-safe comparisons, CSPRNG usage

Numerical Methods

When to use

Diagnosing floating-point precision issues (cancellation, accumulation error, overflow)
Choosing between LU, QR, or SVD decomposition for a linear algebra problem
Implementing root-finding when an analytical solution does not exist
Selecting a numerical integration method based on smoothness and accuracy requirements
Using FFT for polynomial multiplication, convolution, or signal analysis
Reviewing cryptographic primitive usage for correctness and safety

Core principles

Never compare floats with == — always use absolute or relative epsilon; this is not optional
Partial pivoting is not optional in Gaussian elimination — skipping it breaks numerical stability
SVD is the Swiss Army knife — when LU and QR fail or when rank matters, SVD solves it
Brent's method is the default root finder — combines guaranteed convergence with superlinear speed
Never implement your own crypto — use libsodium, OpenSSL, or Web Crypto API; rolling your own is a security incident waiting to happen

Reference Files

references/floating-point-and-matrix.md — IEEE 754 pitfalls, Kahan summation, precision type selection, Gaussian elimination with pivoting, LU/QR/SVD decompositions, sparse matrix formats (COO/CSR/CSC)
references/root-finding-and-integration.md — bisection, Newton-Raphson, secant, Brent's method, trapezoidal/Simpson's/Gaussian quadrature, adaptive integration, Cooley-Tukey FFT, NTT for exact polynomial multiplication
references/cryptographic-foundations.md — secure hash functions (SHA-256, BLAKE3), HMAC, AES-256-GCM, ChaCha20-Poly1305, key derivation (Argon2, bcrypt), RSA/ECDSA/ECDH, timing-safe comparisons, CSPRNG usage