Successive Over-Relaxation
E157387
iterative method for linear systems
iterative numerical method
relaxation method
stationary iterative method
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Successive Over-Relaxation canonical | 3 |
| SSOR | 1 |
| Successive Over-Relaxation method | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1382440 — 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 Over-Relaxation Context triple: [Gauss–Seidel method, relatedTo, Successive Over-Relaxation]
-
A.
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.
-
B.
Picard iteration
Picard iteration is a successive approximation method used to construct solutions to ordinary differential equations and establish their existence and uniqueness.
-
C.
Crank–Nicolson scheme
The Crank–Nicolson scheme is a finite difference method for numerically solving time-dependent partial differential equations, especially parabolic ones like the heat equation, known for its second-order accuracy and unconditional stability.
-
D.
Courant–Friedrichs–Lewy condition
The Courant–Friedrichs–Lewy condition is a fundamental stability criterion in numerical analysis that restricts the time step size in discretized partial differential equations to ensure convergence of the computed solution.
-
E.
Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
- 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 Over-Relaxation Target entity description: 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.
-
A.
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.
-
B.
Picard iteration
Picard iteration is a successive approximation method used to construct solutions to ordinary differential equations and establish their existence and uniqueness.
-
C.
Crank–Nicolson scheme
The Crank–Nicolson scheme is a finite difference method for numerically solving time-dependent partial differential equations, especially parabolic ones like the heat equation, known for its second-order accuracy and unconditional stability.
-
D.
Courant–Friedrichs–Lewy condition
The Courant–Friedrichs–Lewy condition is a fundamental stability criterion in numerical analysis that restricts the time step size in discretized partial differential equations to ensure convergence of the computed solution.
-
E.
Euler’s method for numerical integration
Euler’s method for numerical integration is a simple first-order numerical procedure used to approximate solutions to ordinary differential equations by stepping forward in small increments.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
iterative method for linear systems
ⓘ
iterative numerical method ⓘ relaxation method ⓘ stationary iterative method ⓘ |
| advantage |
low memory requirements
ⓘ
simple to implement ⓘ |
| appliesTo |
discretized partial differential equations
ⓘ
large systems of linear equations ⓘ sparse linear systems ⓘ |
| basedOn | Gauss–Seidel method ⓘ |
| category |
iterative methods for sparse systems
ⓘ
numerical linear algebra ⓘ |
| computes | approximate solution vector x ⓘ |
| convergenceCondition | 0 < ω < 2 for many classes of problems ⓘ |
| convergenceRateDependsOn | spectral radius of iteration matrix ⓘ |
| convergesFasterThan | Gauss–Seidel method for suitable ω ⓘ |
| dependsOn | choice of relaxation factor ω ⓘ |
| generalizes | Gauss–Seidel method ⓘ |
| hasAbbreviation |
SOR
ⓘ
SSOR ⓘ
linked to:
Successive Over-Relaxation
|
| hasGoal | accelerate convergence of Gauss–Seidel ⓘ |
| hasParameter | ω ⓘ |
| hasVariant | Symmetric Successive Over-Relaxation ⓘ |
| introducesParameter | relaxation factor ω ⓘ |
| isLinearIteration | true ⓘ |
| iterationMatrixDependsOn | ω ⓘ |
| limitation |
may converge slowly for ill-conditioned systems
ⓘ
performance sensitive to ω selection ⓘ |
| optimalParameterRange | 1 < ω < 2 for over-relaxation ⓘ |
| reducesTo | Gauss–Seidel method when ω = 1 ⓘ |
| relatedTo |
Gauss–Seidel method
ⓘ
Jacobi method ⓘ Richardson iteration ⓘ Successive Under-Relaxation ⓘ |
| requires |
coefficient matrix A
ⓘ
right-hand side vector b ⓘ |
| specialCaseWhen | ω = 1 gives Gauss–Seidel method ⓘ |
| typicalUseCase | elliptic partial differential equations ⓘ |
| underRelaxationRange | 0 < ω < 1 ⓘ |
| updateFormulaUses |
diagonal part D of A
ⓘ
splitting A = D + L + U ⓘ strictly lower triangular part L of A ⓘ strictly upper triangular part U of A ⓘ |
| updateRule | x^{(k+1)} = x^{(k)} + ω D^{-1}(b − A x^{(k+1,partial)}) ⓘ |
| usedIn |
computational fluid dynamics
ⓘ
engineering simulations ⓘ finite difference methods ⓘ finite element methods ⓘ scientific computing ⓘ |
| 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 Over-Relaxation Description of subject: 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.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Successive Over-Relaxation
linked to: Successive Over-Relaxation