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In graph Frontier
Numerical AnalysisMathematicsEstablished

Iterative method

An iterative method refines a guess step by step toward a solution, as in Newton's method for finding roots.

Iterative methodNumerical approximationFloating-point arithmeticAlgorithmNumerical linear algebraRate of convergenceNewton's methodDifferential equationRound-off error

At a glance

Type
computation
Disciplines 2
Numerical AnalysisMathematics
Mental models 0
—
Role in the graph
Cross-disciplinary bridge
reaches 6 discipline lenses

Key signals

Cross-disciplinary reach
Disciplines
2
  • Numerical Analysis
  • Mathematics
Evidence & development

Dependencies

What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.

Foundations · builds on

Iterative methoddepends onRate of convergenceEstablished

Open Rate of convergence →

Iterative method depends on Rate of convergence.

System context

Iterative methodis aAlgorithmEstablished

Open Algorithm →

An iterative method is an algorithm.

Mechanism: It repeats an improvement step, each pass moving the estimate closer to the true answer.

Newton's methodis aIterative methodEstablished

Open Newton's method →

Newton's method is a kind of Iterative method.

Structural role & consequence

Interpreted from the current atlas graph — what the connections mean, not just how many there are.

  • Currently dark in the atlas: no key date stored · 6 of 6 of its relations lack claim-level evidence.

    atlas representation · Describes the current Thinking OS representation, not the state of the world.

  • Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).

    structural · Structural graph analysis — not a claim of importance, causation or history.

  • Structural neighbourhood: 6 → 28 → 97 concepts reachable within 3 hops.

    structural · Structural reach — being reachable is not the same as being understood.

  • All 6 of its relationships stay within its own discipline — a field-specific concept in the current atlas.

    structural · Structural graph analysis — not a claim of importance, causation or history.

0%

cross-field
6 within-field, 0 cross-field

0 of 6 relations carry evidence · concept has a verified source

Strengths & constraints

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
  • No dated history stored — the atlas records no key date for this concept. atlas representation

Conditions

  • Its dependency reading rests on 1 foundation relation. structural
  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Dependency radial

What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.

Rate of convergenceIterative method◀ builds onenables ▶

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Numerical Analysis

Through this lens it connects to Numerical approximation, Numerical linear algebra, Rate of convergence and Newton's method.

Iterative method through the Numerical Analysis lens →

Mathematics

Through this lens it connects to Algorithm, Numerical approximation and Floating-point arithmetic.

Iterative method through the Mathematics lens →

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

The scientific picture
  • Connects 6 other ideas across 2 disciplines.
  • A cross-disciplinary bridge — its connections reach into 6 other fields.
  • Most of its connections are of the “Kind & structure” kind.

Derived from the graph’s real structure — observations, not a score.

Sources