projected non-stationary simultaneous iterative methods

Projected non-stationary simultaneous iterative methods

In this paper, we study Projected non-stationary Simultaneous It-erative Reconstruction Techniques (P-SIRT). Based on algorithmic op-erators, convergence result are adjusted with Opial’s Theorem. The advantages of P-SIRT are demonstrated on examples taken from to-mographic imaging.

Sparse Tiling for Stationary Iterative Methods

In modern computers, a program’s data locality can affect performance significantly. This paper details full sparse tiling, a run-time reordering transformation that improves the data locality for stationary iterative methods such as Gauss–Seidel operating on sparse matrices. In scientific applications such as finite element analysis, these iterative methods dominate the execution time. Full sp...

CAAM 454/554: Stationary Iterative Methods

Stationary iterative methods for solving systems of linear equations are considered by some as out of date and out of favor, as compared to methods based on Krylov subspace iterations. However, these methods are still useful in many circumstances because they are easier to implement and, more importantly, can be used as pre-conditioners in combination with Krylov-subspace methods. In this note,...

Componentwise Error Analysis for Stationary Iterative Methods∗

How small can a stationary iterative method for solving a linear system Ax = b make the error and the residual in the presence of rounding errors? We give a componentwise error analysis that provides an answer to this question and we examine the implications for numerical stability. The Jacobi, Gauss-Seidel and successive overrelaxation methods are all found to be forward stable in a componentw...

Iterative methods for solving non linear Fokker-Planck equation

Low-rank Iterative Methods for Projected Generalized Lyapunov Equations

LOW-RANK ITERATIVE METHODS FOR PROJECTED GENERALIZED LYAPUNOV EQUATIONS TATJANA STYKEL Abstract. We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximat...