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algorithm Gauss–Seidel method is inputs: A, b output: φ Choose an initial guess φ to the solution repeat until convergence for i from 1 until n do σ ← 0 for j from 1 until n do if j ≠ i then σ ← σ + a ij φ j end if end (j-loop) φ i ← (b i − σ) / a ii end (i-loop) check if convergence is reached end (repeat)
The Gauss-Seidel, the Jacobi variants and transmission line modelling, TLM. The names of the first two methods are derived from the structural similarities to the numerical methods by the same name. The reason is that the Jacobi method is easy to convert into an equivalent parallel algorithm while there are difficulties to do so for the Gauss ...
In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as Voltage, voltage angles, real power and reactive power.
Relaxation methods are used to solve the linear equations resulting from a discretization of the differential equation, for example by finite differences. [ 2 ] [ 3 ] [ 4 ] Iterative relaxation of solutions is commonly dubbed smoothing because with certain equations, such as Laplace's equation , it resembles repeated application of a local ...
The slack bus is crucial to a load flow problem since it will account for transmission line losses. In a load flow problem, conservation of energy results in the total generation equaling to the sum of the loads. However, there still would be a discrepancy in these quantities due to line losses, which are dependent on line current.
Other notable examples include solving partial differential equations, [1] the Jacobi kernel, the Gauss–Seidel method, [2] image processing [1] and cellular automata. [3] The regular structure of the arrays sets stencil techniques apart from other modeling methods such as the Finite element method .
In numerical linear algebra, the method of successive over-relaxation (SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process.
kernel smoothing methods; more complex operators, such as surface smoothers for second and higher-order interactions; In theory, step (b) in the algorithm is not needed as the function estimates are constrained to sum to zero. However, due to numerical issues this might become a problem in practice. [1]