Related papers: Comparative analysis of Jacobi and Gauss-Seidel it…
The main goal of this paper is to generalize Jacobi and Gauss-Seidel methods for solving non-square linear system. Towards this goal, we present iterative procedures to obtain an approximate solution for non-square linear system. We derive…
The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly…
It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices…
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…
Solving a set of simultaneous linear equations is probably the most important topic in numerical methods. For solving linear equations, iterative methods are preferred over the direct methods especially when the coefficient matrix is…
This work wishes to support various mathematical issues concerning the iterative methods with the help of new programming languages. We consider a way to show how problems in math have an answer by using different academic resources and…
We propose fork-join and task-based hybrid implementations of four classical linear algebra iterative methods (Jacobi, Gauss-Seidel, conjugate gradient and biconjugate gradient stabilised) as well as variations of them. Algorithms are duly…
In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…
This paper deals with investigating numerical methods for solving coupled system of nonlinear parabolic problems. We utilize block monotone iterative methods based on Jacobi and Gauss--Seidel methods to solve difference schemes which…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
This paper investigates numerical methods for solving coupled system of nonlinear elliptic problems. We utilize block monotone iterative methods based on Jacobi and Gauss--Seidel methods to solve difference schemes which approximate the…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…
We present a scalability study of Golub-Kahan bidiagonalization for the parallel iterative solution of symmetric indefinite linear systems with a 2x2 block structure. The algorithms have been implemented within the parallel numerical…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
We propose a simple doubly stochastic block Gauss--Seidel algorithm for solving linear systems of equations. By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber…
The Gauss-Seidel method has been used for more than 100 years as the standard method for the solution of linear systems of equations under certain restrictions. This method, as well as Cramer and Jacobi, is widely used in education and…
A new one-parameter family of iterative method for solving nonlinear equations is constructed and studied. Two variants, both with cubic convergence, are developed, one for finding simple zeros and other for multiple zeros of known…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…