numerical-methods

Identify and mitigate numerical stability issues in statistical computations with R and math snippets.

Updated Aug 27, 2026

Search Tags:#gradient #softmax-stability #hessian #QR-decomposition #numerical-stability #log-sum-exp #Monte-Carlo

Ready to run

npx skills add https://github.com/Data-Wise/scholar --skill numerical-methods

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: numerical-methods
Source: https://github.com/Data-Wise/scholar/tree/main/src/plugin-api/skills/implementation/numerical-methods
Command: npx skills add https://github.com/Data-Wise/scholar --skill numerical-methods

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

This Skill provides guidelines and practical techniques to identify, prevent, and diagnose numerical stability issues in statistical computations, improving accuracy and reliability of results.

Core Features & Use Cases

Floating-point fundamentals: Understand precision, range, and machine epsilon to design robust computations.
Stability patterns: Apply log-sum-exp, softmax stabilization, and proper variance/gradient calculations.
Robust linear algebra: Use QR/Cholesky decompositions and pseudoinverse to avoid ill-conditioning in regression and optimization.
Applications: Useful in estimators, optimization routines, Monte Carlo simulations, and numerical integration.

Quick Start

Run a quick check on a sample dataset to validate stability of a simple log-sum-exp, then report any instability and suggested fixes.

Frequently Asked Questions about numerical-methods

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I fix numerical instability in softmax and log-sum-exp calculations?▼

To fix numerical instability in softmax and log-sum-exp calculations, apply stabilization patterns that shift the exponent before evaluation, preventing overflow and underflow in floating-point arithmetic. This skill provides the exact formulas and R snippets needed to implement these robust routines safely.

What causes ill-conditioning in optimization and how do I solve it?▼

Ill-conditioning in optimization arises from near-singular matrices, causing unstable gradients and Hessian computations. You solve it by replacing standard matrix inversions with robust linear algebra techniques like QR or Cholesky decompositions, which this skill details with practical code examples.

When do I need to check floating-point precision and machine epsilon in statistical estimators?▼

You need to check floating-point precision and machine epsilon in statistical estimators when working with very large or small numbers, which can cause silent precision loss. This skill provides guidelines to diagnose these issues and ensure computation accuracy in Monte Carlo simulations and integration.

Does this numerical stability skill work with R and provide practical code examples?▼

Yes, this numerical stability skill works with R and provides practical math and R code snippets to enforce stable log-sum-exp, conditioning checks, and robust numerical routines for your optimization and simulation workflows.

Why are my Monte Carlo simulations returning NaN or infinite values?▼

Monte Carlo simulations return NaN or infinite values due to floating-point limits being exceeded during exponential or probability calculations. This skill helps you identify these numerical stability issues and mitigate them using stable computation patterns and proper variance calculations.