A numerical-method is a human-made procedure for solving mathematical problems through numerical approximation rather than exact symbolic computation. It operates on discretized representations of continuous problems, trading analytical precision for computational tractability. Parameters: (1) input is a mathematical problem amenable to discretization, (2) output is an approximate solution within bounded error, (3) the method specifies an algorithmic sequence of arithmetic operations. Persistence mechanism: mathematical literature, computational libraries, and engineering practice encode and propagate these methods across generations. [formal: numericus | substrate: mind | horizon: generations | explicit: yes | epoch: 0.01]
Accepted ontology entry
numerical-method
A numerical-method is a human-made procedure for solving mathematical problems through numerical approximation rather than exact symbolic computation. It operates on discretized representations of continuous problems, trading analytical pr…
Definition
Why it is in scope
A human-made method for solving mathematical problems through numerical approximation rather than symbolic computation. Built to persist via mathematical practice, textbooks, and computational software.
Names and aliases
- numerical-methoden · CANONICAL
Relations from this entry
- cmr9lxelr009uhcxflfegr6mfINSTANCE_OF →
A numerical method is a specific kind of algorithm — a step-by-step procedure for numerical computation. A competent speaker would call a numerical method 'a kind of algorithm.' Law 9: specific→general. Algorithm is the nearest kind (more specific than 'procedure' or 'method').
- cmrg4vstb00kx2a1nar61eoe7DEPENDS_ON →
Numerical-method DEPENDS_ON mathematics: remove mathematics and numerical methods stop operating entirely. Numerical methods are computational techniques for solving mathematical problems (root-finding, integration, differential equations, linear systems). Their algorithms, convergence criteria, error bounds, and all their operations are defined in mathematical terms. Without mathematics, numerical methods are not merely unsayable — they cease to function as procedures for approximate mathematical computation. The removal test passes: X needs Y to operate now (Law 8, 8b).
Relations to this entry
- log-sum-exp← INSTANCE_OF
log-sum-exp IS a specific kind of numerical method — it is a technique for computing log(sum(exp(x))) in a numerically stable way. The nearest kind is numerical-method: a procedure for approximating mathematical computations. Direction is specific→general.
Record identity
- Created
- Jul 22, 2026, 8:40 PM UTC
- Content hash
- 89b4bcb020f238174b13111fe975abb65d19cb51dcff15dc4d4a14ca68879df9