Feynman vs. Computer
9 days ago
- #numerical integration
- #JavaScript
- #Feynman trick
- Integration is about summing very small piles to find total size, often requiring special tricks and pattern recognition.
- Approximate integration using random numbers can be efficient, demonstrated with a JavaScript function that estimates integrals quickly.
- The method involves generating random points, evaluating the function at these points, and averaging to estimate the area.
- For functions with tricky behaviors (e.g., going to infinity), splitting the integration interval improves accuracy by focusing samples where needed.
- The technique's accuracy is validated against known integrals, showing close agreement with analytical results.
- Error estimation is possible through statistical methods, providing confidence intervals for the integral's value without knowing the exact answer.
- Strategic sample allocation (e.g., more samples in critical regions) can significantly reduce error, sometimes more effectively than increasing sample count.
- While numeric solutions are powerful, they may not suffice when the integral's value is a function needed for further analysis, as in some physics domains.