Iterative methods for solving linear systems - Greenbaum - 1997 () Citation Context ...ected gradient method (Chu and Driessel 1990), the interior point method (Karmarkar 1984, Wright 1997, Potra and Wright 2000, Wright 2005) or the conjugate gradient method (Hestenes and Stiefel 1952, =-=...
Iterative Methods for Solving Linear Systems 175 necessarily entail the explicit knowledge of the matrix A. In other words, an iterative method of solving Ax = f can also be realized when the system is specified in an operator form. Building the iteration sequence does not require choosing ...
There are two types of methods for solving linear equationsA*x = b: Direct methodsare variants of Gaussian elimination. These methods use the individual matrix elements directly, through matrix operations such as LU, QR, or Cholesky factorization. You can use direct methods to solve linear equati...
An iterative method along with its convergence analysis is developed for solving singular linear systems with index one. Necessary and sufficient conditions along with the estimation of error bounds for the unique solution are derived. Four numerical examples including singular square M-matrix, randomly...
In this paper the systolic design for the Accelerated Overrelaxation iterative method [1] for solving large linear systems of linear equations is presented based on the VLSI techniques discussed earlier in Evans and Haider [2] for the Jacobi, Gauss-Seidel, S.O.R. and S.S.O.R. methods....
Iterative Methods for Sparse Linear Systems The first iterative methods used for solving large linear systems were based on relaxation of the coordinates. Beginning with a given approximate solution, these methods modify the components of the approximation, one or a few at a time ... Y Saad 被...
NumericalAnalysisLectureNotes PeterJ.Olver 7.IterativeMethodsforLinearSystems Lineariterationcoincideswithmultiplicationbysuccessivepowersofamatrix;con- vergenceoftheiteratesdependsonthemagnitudeofitseigenvalues.Wediscussinsome detailavarietyofconvergencecriteriabasedonthespectralradius,onmatrixnorms,and oneigenvalueestima...
Iterative methods for solving sparse linear systems with a parallel preconditioner The incomplete LU factorization is one of the more effective preconditioner of the conjugate gradient-type methods in connection with the solution of large... G Zilli - 《International Journal of Computer Mathematics》 被...
The first iterative methods used for solving large linear systems were based on relaxation of the coordinates. Beginning with a given approximate solution, these methods modify the components of the approximation, one or a few at a time and in a certain order, until convergence is reached. Each...
Here we separate two variables U and Enr, so that we change the problems into solving the smaller scale equations iteratively. The new program can be easily applied. Finally, numerical examples show that the proposed method is more efficient than common methods; we compare the L 2 -error and...