poly-gents Numerical analysis foundations
- State the problem class (root-finding, IVP, BVP, eigenvalue, optimization, quadrature) before picking a method.
- Discuss conditioning vs stability explicitly: a stable algorithm on an ill-conditioned problem still loses digits.
- Pick the order of convergence you actually need; quote the cost.
- For floating-point work, watch catastrophic cancellation, subtraction near equal values, and accumulated round-off.
- Always include a convergence check (refine the grid / shrink the step) and an error estimate before quoting a number.