A Linearly Convergent Doubly Stochastic Gauss-Seidel Algorithm for Solving Linear Equations and A Certain Class of Over-Parameterized Optimization Problems.Consider the classical problem of solving a general linear system of\nequations $Ax=b$. It is well known that the (successively over relaxed)\n...
EQUATIONS, SimultaneousNumerical solutionsAn interesting new partitioning algorithm for solving simultaneous linear equations is presented. The partitioning algorithm consists of a procedure called matrix reduction which is followed by back substitution. During the matrix reduction procedure the algorithm ...
The proposed algorithm is aimed at both increased inherent parallelism and reduced computational effort It has been shown that the solutions can be obtained in (2n—1) time steps for an nth order system of linear equations, against (3n—2) time steps required in the most acknowledged GE-...
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and and an vector b, find a vector x such that Ax=b. Often, one does not need to know the solution x itself, but rather an approximatio...
the algorithm is applicable to both heat and Poisson’s equations comparing to their analytical solutions. The outline of this paper is as follows. In Sect.2, we supply auxiliary tools to solve linear matrix equations and to make a convergence analysis of an iterative method for solving such ...
For large scale of sparse linear equations, due to the efficiency requirement and computer memory limitation, iterative algorithms are often used. There are two major types of iterative algorithms for solving linear equations: stationary methods and non-stationary methods. Both can be interpreted in ...
A quantum-behaved particle swarm optimization algorithm is presented in this paper for solving nonlinear equations. The positions of particle are coded by probability amplitudes of qubits that are updated by quantum rotation gates in this method. The corresponding real number solution at specified interv...
Quantumalgorithmforlinearsystemsof equations AramW.Harrow ∗ ,AvinatanHassidim † andSethLloyd ‡ June2,2009 Abstract Solvinglinearsystemsofequationsisacommonproblemthatarises bothonitsownandasasubroutineinmorecomplexproblems:givena matrixAandavector b,findavectorxsuchthatAx= b.Weconsider thecasewhere...
A new algorithm based on Givens rotations for solving linear equations on fault-tolerant mesh... Studies an input/output overhead free Givens rotations based parallel algorithm for solving a system of linear equations. What the algorithm uses; Importan... Balasubramanya,N K.,Bhuvaneswari,... -...
NOTE: Mac OSX users will need to installOpenMPin order to compile the package. Checkherefor a solution. Functions cgsolve Conjugate gradient method for solving system of linear equations Ax = b, where A is symmetric and positive definite, b is a column vector. ...