\| (\d\d) | $1
\| (\d\d\d) | $1
Мы проверили 11 вариантов базиса полинома.
Выбор базиса полиномов имеет огромное значение для формы кривой, численной устойчивости аппроксимации и качества её соответствия.
| Basis Name | Handles Curves Well | Repeating Patterns | Extremes / Outliers | Growth/Decay | Best Data Shape / Domain |
|---|---|---|---|---|---|
| Chebyshev | Good | No | No | Poor | Smooth curves, bounded |
| Fourier | Fair | Yes | No | Poor | Periodic signals |
| Hermite | Good | No | Yes | Yes | Bell-shaped, any range |
| Laguerre | Good | No | Yes | Yes | Decaying, positive-only |
| Legendre | Fair | No | No | Poor | Smooth curves, bounded |
| Logarithmic | Fair | No | Yes | Yes | Logarithmic growth |
| Monomial | Poor | No | No | Poor | Any simple trend |