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name: numerical-analysis-foundations description: "Floating point, conditioning, stability, convergence, error budgets, choosing a scheme."

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.