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...

Algorithm 1 Seidel(A, b, c) 1: if there is only one variable then 2: Treat all inequalities in Ax ≤ b as equalities and solve for x in each. 3: Return the point out of these that maximizes c. 4: end if 5: if there are as many constraints as variables then 6: Solve the linear system Ax = b using Gaussian elimination and return the resulting point. 7: end if 8: Pick a constraint h : aix ≤ bi unif...

The Jacobi and Gauss-Seidel iterative methods are among iterative methods for solving linear system of equations. In this paper, a new iterative method is introduced, it is based on the linear combination of old and most recent calculated solutions. The new method can be considered as a general method, where the Jacobi and Gauss-Seidel methods as two special cases of it. Some convergence proper...

A parallel variant of the block Gauss-Seidel iteration for the solution of block-banded linear systems is presented. The coefficient matrix is partitioned among the processors ss in the domain decomposition methods and then it is split so that the resulting iterative method has the same spectral properties of the block Gauss-Seidel iteration. The parallel algorithm is applied to the solution of...

We consider coordinate descent methods on convex quadratic problems, in which exact line searches are performed at each iteration. (This algorithm is identical to Gauss-Seidel on the equivalent symmetric positive definite linear system.) We describe a class of convex quadratic problems for which the random-permutations version of cyclic coordinate descent (RPCD) outperforms the standard cyclic ...

This work is based on the Euler-Seidel matrix method [11] which is related to algorithms, combinatorics and generating functions. This method is quite useful to investigate properties of some special numbers and polynomials. In this paper we consider the Euler-Seidel matrix method for some combinatorial numbers and polynomials. This method is relatively easier than the most of combinatorial met...

The Randomized Gauss-Seidel Method (RGS) is an iterative algorithm that solves overdetermined systems of linear equations Ax = b. This paper studies an update on the RGS method, the Randomized Block Gauss-Seidel Method(RBGS). At each step, the algorithm greedily minimizes the objective function L(x) = kAx bk2 with respect to a subset of coordinates. This paper describes a Randomized Block Gauss...

On May 8 2001, Jaap Seidel passed away. This volume of the European Journal of Combinatorics is dedicated to his memory. Jaap Seidel loved Mathematics. He wanted to learn it, to understand it, and most of all to teach it. In his courses and personal contacts he was very inspiring. Many mathematicians, especially young ones, were influenced by Jaap. Besides being a teacher, he was also very inte...