Successive Under-Relaxation
E621091
Successive Under-Relaxation is a numerical technique for iteratively solving linear systems that deliberately uses a relaxation factor less than one to slow updates and improve stability or convergence in certain problems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Successive Under-Relaxation canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6833242 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Successive Under-Relaxation Context triple: [Successive Over-Relaxation, relatedTo, Successive Under-Relaxation]
-
A.
Successive Over-Relaxation
Successive Over-Relaxation is an iterative numerical method that accelerates the convergence of the Gauss–Seidel algorithm for solving large systems of linear equations by introducing a relaxation factor.
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B.
Gauss–Seidel method
The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
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C.
Richardson iteration
Richardson iteration is an early iterative method for solving linear systems and other operator equations, based on repeated relaxation steps to progressively improve an approximate solution.
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D.
Jacobi method
The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
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E.
Picard iteration
Picard iteration is a successive approximation method used to construct solutions to ordinary differential equations and establish their existence and uniqueness.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Successive Under-Relaxation Target entity description: Successive Under-Relaxation is a numerical technique for iteratively solving linear systems that deliberately uses a relaxation factor less than one to slow updates and improve stability or convergence in certain problems.
-
A.
Successive Over-Relaxation
Successive Over-Relaxation is an iterative numerical method that accelerates the convergence of the Gauss–Seidel algorithm for solving large systems of linear equations by introducing a relaxation factor.
-
B.
Gauss–Seidel method
The Gauss–Seidel method is an iterative numerical technique used to solve systems of linear equations, particularly in large, sparse problems arising in scientific and engineering computations.
-
C.
Richardson iteration
Richardson iteration is an early iterative method for solving linear systems and other operator equations, based on repeated relaxation steps to progressively improve an approximate solution.
-
D.
Jacobi method
The Jacobi method is an iterative numerical algorithm used to solve systems of linear equations by repeatedly updating each variable using values from the previous iteration.
-
E.
Picard iteration
Picard iteration is a successive approximation method used to construct solutions to ordinary differential equations and establish their existence and uniqueness.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf | iterative numerical method ⓘ |
| alsoKnownAs | SUR ⓘ |
| appliesTo |
discretized partial differential equations
ⓘ
linear algebraic systems ⓘ |
| belongsTo |
iterative methods for sparse systems
ⓘ
numerical linear algebra ⓘ |
| canBeCombinedWith |
Gauss–Seidel iteration
ⓘ
linked to:
Gauss–Seidel method
Jacobi iteration ⓘ |
| contrastsWith | Successive Over-Relaxation which uses omega > 1 ⓘ |
| dependsOn | choice of relaxation factor for performance ⓘ |
| goal | to obtain stable convergence for difficult systems ⓘ |
| hasConstraintOnParameter | 0 < omega < 1 ⓘ |
| hasEffect |
increases robustness of convergence
ⓘ
reduces step size of each iteration ⓘ |
| hasMathematicalForm | x^{k+1} = x^{k} + omega (x^{k+1}_{*} - x^{k}) ⓘ |
| hasParameter | omega ⓘ |
| hasProperty |
can prevent divergence in unstable schemes
ⓘ
can slow nominal convergence rate ⓘ damps oscillations in iterative updates ⓘ relaxation factor less than one ⓘ |
| hasPurpose |
to improve convergence behavior in some problems
ⓘ
to improve stability of iterative schemes ⓘ to iteratively solve linear systems ⓘ |
| isBasedOn | relaxation techniques ⓘ |
| isRelatedTo |
Gauss–Seidel method
ⓘ
Jacobi method ⓘ Successive Over-Relaxation ⓘ |
| isUsedIn |
computational fluid dynamics
ⓘ
engineering simulations ⓘ finite difference methods ⓘ finite element methods ⓘ finite volume methods ⓘ iterative solution of Poisson equations ⓘ steady-state solvers ⓘ |
| modifies | update step of an iterative method ⓘ |
| optimizationCriterion | trade-off between stability and speed of convergence ⓘ |
| typicalUseCase |
highly nonlinear or stiff problems
ⓘ
strongly coupled equations ⓘ |
| usesConcept | relaxation factor ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Successive Under-Relaxation Description of subject: Successive Under-Relaxation is a numerical technique for iteratively solving linear systems that deliberately uses a relaxation factor less than one to slow updates and improve stability or convergence in certain problems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.