SOR
E621090
SOR is an iterative numerical method used to accelerate the convergence of solving large systems of linear equations, particularly in scientific and engineering computations.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
iterative numerical method
ⓘ
linear system solver ⓘ |
| advantage | simple to implement ⓘ |
| alsoCalled | over-relaxation method ⓘ |
| analyzedUsing | spectral radius of iteration matrix ⓘ |
| appliedTo |
Poisson equation
NERFINISHED
ⓘ
discretized partial differential equations ⓘ elliptic PDEs ⓘ sparse linear systems ⓘ |
| assumes | linear system Ax = b ⓘ |
| basedOn | Gauss–Seidel method NERFINISHED ⓘ |
| belongsTo | numerical linear algebra ⓘ |
| canBe |
over-relaxation when relaxation factor is greater than 1
ⓘ
under-relaxation when relaxation factor is less than 1 ⓘ |
| canBeCombinedWith | multigrid methods ⓘ |
| category | stationary iterative method ⓘ |
| convergenceDependsOn |
choice of relaxation factor
ⓘ
spectral radius of iteration matrix ⓘ |
| convergesIf | spectral radius of iteration matrix is less than 1 ⓘ |
| fullName | Successive Over-Relaxation NERFINISHED ⓘ |
| generalizationOf | Gauss–Seidel method (when relaxation factor equals 1) NERFINISHED ⓘ |
| goal | reduce number of iterations to reach a given accuracy ⓘ |
| hasParameter | relaxation factor ⓘ |
| improves | rate of convergence compared to Gauss–Seidel ⓘ |
| iterationMatrixDependsOn | matrix splitting A = D - L - U ⓘ |
| limitation | may converge slowly for poorly conditioned systems ⓘ |
| modifies | Gauss–Seidel iteration with relaxation factor ⓘ |
| oftenUsedIn |
computational fluid dynamics
ⓘ
computational physics ⓘ finite difference methods ⓘ finite element methods ⓘ |
| oftenUsedWith | grid-based discretizations ⓘ |
| performanceAffectedBy |
matrix conditioning
ⓘ
problem size ⓘ |
| relatedTo |
Conjugate Gradient method
NERFINISHED
ⓘ
Gauss–Seidel method NERFINISHED ⓘ Jacobi method NERFINISHED ⓘ |
| requires |
iterative update of solution vector
ⓘ
splitting of coefficient matrix ⓘ |
| specialCaseOf | relaxation methods ⓘ |
| tunedBy | experimentally chosen relaxation factor ⓘ |
| typicalRelaxationFactorRange | between 1 and 2 for over-relaxation ⓘ |
| typicalUseCase | large, sparse, structured linear systems ⓘ |
| usedFor |
accelerating convergence of iterative methods
ⓘ
solving large systems of linear equations ⓘ |
| usedIn |
engineering computations
ⓘ
scientific computations ⓘ |
Referenced by (1)
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