Gauss–Seidel method ≈ Gauss–Seidel method
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Phaseless Recovery Using the Gauss–Newton Method Open
In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then upda…
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Load Flow Analysis on IEEE 14 Bus System Open
This article presents a load flow analysis of an IEEE14 BUS system using the Newton-Raphson method, which simplifies the analysis of load balancing problems. The software used for the programming platform is MATLAB. This paper gives an ove…
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A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors Open
This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and…
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Two new generalized iteration methods for solving absolute value equations using $ M $-matrix Open
In this paper, we present two new generalized Gauss-Seidel iteration methods for solving absolute value equations $ Ax-| x | = b, $ where $ A $ is an $ M $-matrix. Furthermore, we demonstrate their convergence under specific assumptions. N…
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Optimal power dispatch of DGS in DC power grids: A hybrid gauss-seidel-genetic-algorithm methodology for solving the OPF problem Open
This paper addresses the optimal power flow (OPF) problem in direct current (DC) power grids via a hybrid Gauss-Seidel-Genetic-Algorithm methodology through a master-slave optimization strategy. In the master stage, a genetic algorithm is …
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Solutions of First-Order Volterra Type Linear Integrodifferential Equations by Collocation Method Open
The numerical solutions of linear integrodifferential equations of Volterra type have been considered. Power series is used as the basis polynomial to approximate the solution of the problem. Furthermore, standard and Chebyshev-Gauss-Lobat…
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A Finite Difference Method and Effective Modification of Gradient Descent Optimization Algorithm for MHD Fluid Flow over a Linearly Stretching Surface Open
Present contribution is concerned with the construction and application of a numerical method for the fluid flow problem over a linearly stretching surface with the modification of standard Gradient descent Algorithm to solve the resulted …
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On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence Open
This paper presents a general formulation of the classical iterative-sweep power flow, which is widely known as the backward–forward method. This formulation is performed by a branch-to-node incidence matrix with the main advantage that th…
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Worst-case Complexity of Cyclic Coordinate Descent: $O(n^2)$ Gap with Randomized Version Open
This paper concerns the worst-case complexity of cyclic coordinate descent (C-CD) for minimizing a convex quadratic function, which is equivalent to Gauss-Seidel method and can be transformed to Kaczmarz method and projection onto convex s…
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Iterative Methods for Solving a System of Linear Equations in a Bipolar Fuzzy Environment Open
We develop the solution procedures to solve the bipolar fuzzy linear system of equations (BFLSEs) with some iterative methods namely Richardson method, extrapolated Richardson (ER) method, Jacobi method, Jacobi over-relaxation (JOR) method…
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Numerical Methods for Solving Fuzzy Linear Systems Open
In this article, three numerical iterative schemes, namely: Jacobi, Gauss–Seidel and Successive over-relaxation (SOR) have been proposed to solve a fuzzy system of linear equations (FSLEs). The convergence properties of these iterative sch…
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Efficient Parallel Implementations of Sparse Triangular Solves for GPU Architectures Open
The sparse triangular matrix solve (SpTrSV) is an important computation kernel that is demanded by a variety of numerical methods such as the Gauss-Seidel iterations. However, developing efficient parallel algorithms for SpTrSV that are su…
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Comparison Of Newton Raphson And Gauss Seidel Methods For Power Flow Analysis Open
This paper presents a comparative study of the Gauss Seidel and Newton-Raphson polar coordinates methods for power flow analysis. The effectiveness of these methods are evaluated and tested through a different IEEE bus test system on the b…
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Analysis Local Convergence of Gauss-Newton Method Open
The Gauss-Newton method is a very efficient, simple method used to solve nonlinear least-squares problems. This can be seen as a modification of the newton method to find the minimum value of a function. In solving nonlinear problems, the …
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Power Flow Analysis Open
Power flow, or load flow, is widely used in power system operation and planning. The power flow model of a power system is built using the relevant network, load, and generation data. Outputs of the power flow model include voltages at dif…
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Optimal Allocation of Distributed Generation with Reconfiguration by Genetic Algorithm Using Both Newton Raphson and Gauss Seidel Methods for Power Losses Minimizing Open
The power loss in electrical networks is considered unavoidable, because of its inherent resistance, for effective and economical operation; network loss should be reduced to maximum extent.There are two goals for this study, the first one…
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Low-complexity signal detection networks based on Gauss-Seidel iterative method for massive MIMO systems Open
In massive multiple-input multiple-output (MIMO) systems with single- antenna user equipment (SAUE) or multiple-antenna user equipment (MAUE), with the increase of the number of received antennas at base station, the complexity of traditio…
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Solving non-LTE problems in rotational transitions using the Gauss–Seidel method and its implementation in the Atmospheric Radiative Transfer Simulator Open
This article presents our implementation of a non-LTE solver in spherical symmetry for molecular rotational transition in static or expanding atmospheres. The new open-source code relies on the Gauss–Seidel Accelerated Lambda Iteration met…
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Fast Model-Fitting of Bayesian Variable Selection Regression Using the Iterative Complex Factorization Algorithm Open
Bayesian variable selection regression (BVSR) is able to jointly analyze genome-wide genetic datasets, but the slow computation via Markov chain Monte Carlo (MCMC) hampered its wide-spread usage. Here we present a novel iterative method to…
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Subcell finite volume multigrid preconditioning for high-order discontinuous Galerkin methods Open
We suggest a new multigrid preconditioning strategy for use in Jacobian-free Newton–Krylov (JFNK) methods for the solution of algebraic equation systems arising from implicit Discontinuous Galerkin (DG) discretisations. To define the new p…
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Second-refinement of Gauss-Seidel iterative method for solving linear system of equations Open
Although large and sparse linear systems can be solved using iterative methods, its number of iterations is relatively large. In this case, we need to modify the existing methods in order to get approximate solutions in a small number of i…
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Gauss–Seidel method with oblique direction Open
In this paper, a Gauss–Seidel method with oblique direction (GSO) is proposed for finding the least-squares solution to a system of linear equations, where the coefficient matrix may be full rank or rank deficient and the system is overdet…
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Application of the backward/forward sweep method for solving the power flow problem in DC networks with radial structure Open
This paper presents the application of the backward/forward sweep iterative method for solving the power flow problem in direct current networks with radial structure, considering resistive and constant power loads. The validation of the e…
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Efficient Soft-Output Gauss-Seidel Data Detector for Massive MIMO Systems Open
For massive multiple-input multiple-output (MIMO) systems, linear minimum mean-square error (MMSE) detection has been shown to achieve near-optimal performance but suffers from excessively high complexity due to the large-scale matrix inve…
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Shifted Jacobi collocation method for solving multi-dimensional fractional Stokes’ first problem for a heated generalized second grade fluid Open
This paper reports a new spectral collocation technique for solving fractional Stokes' first problem for a heated generalized second grade fluid (FSFP-HGSGF). We develop a collocation scheme to approximate FSFP-HGSGF by means of the shifte…
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Breaking Locality Accelerates Block Gauss-Seidel Open
Recent work by Nesterov and Stich showed that momentum can be used to accelerate the rate of convergence for block Gauss-Seidel in the setting where a fixed partitioning of the coordinates is chosen ahead of time. We show that this setting…
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Steady-State Analysis of Electrical Networks in Pandapower Software: Computational Performances of Newton–Raphson, Newton–Raphson with Iwamoto Multiplier, and Gauss–Seidel Methods Open
At the core of every system for the efficient control of the network steady-state operation is the AC-power-flow problem solver. For local distribution networks to continue to operate effectively, it is necessary to use the most powerful a…
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Improved Gauss–Seidel detector for large‐scale MIMO systems Open
Large‐scale multiple‐input multiple‐output (LS‐MIMO) is one of the promising technologies beyond the 5G cellular system in which large antenna arrays at the base station (BS) improve the system capacity and energy‐efficiency. However, the …
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Optimal Preconditioning for the Interval Parametric Gauss–Seidel Method Open
We deal with an interval parametric system of linear equations, and focus on the problem how to find an optimal preconditioning matrix for the interval parametric Gauss–Seidel method. The optimality criteria considered are to minimize the …
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High-Precision Iterative Preconditioned Gauss–Seidel Detection Algorithm for Massive MIMO Systems Open
Signal detection is a serious challenge for uplink massive multiple-input multiple-output (MIMO) systems. The traditional linear minimum-mean-squared error (MMSE) achieves good detection performance for such systems, but involves matrix in…