Gaussian elimination is a canonical linear algebra procedure for solving linear systems of equations. In the last few years, the algorithm has received a lot of attention in an attempt to improve its parallel performance. This article surveys recent developments in parallel implementations of Gaussian elimination for shared memory architecture. Five different flavors are investigated. Three of ...

We describe parallel implementations of LU factorization with pivoting for multicore architectures. Implementations that differ in two different dimensions are discussed: (1) using classical partial pivoting versus recently proposed incremental pivoting and (2) extracting parallelism only within the Basic Linear Algebra Subprograms versus building and scheduling a directed acyclic graph of task...

The statistical approach to machine translation (MT) relies heavily on large parallel corpora. For many language pairs, this can be a significant obstacle. A promising alternative is pivoting, i.e. making use of a third language to support the translation. There are a number of pivoting methods, but unfortunately, they were not evaluated in comparable settings. We focus on one particular langua...

We study several solvers for the solution of general linear systems where the main objective is to reduce the communication overhead due to pivoting. We first describe two existing algorithms for the LU factorization on hybrid CPU/GPU architectures. The first one is based on partial pivoting and the second uses a random preconditioning of the original matrix to avoid pivoting. Then we introduce...

Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as a means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by μn < 3 n−1, as compared to 2n−1 for the standard partial pivoting. This bound μ...

Quasi-polar spaces are sets of points having the same intersection numbers with respect to hyperplanes as classical polar spaces. Non-classical examples quasi-quadrics have been constructed using a technique called {\em pivoting} in paper by De Clerck, Hamilton, O'Keefe and Penttila. We introduce more general notion pivoting, switching, also extend this Hermitian The main result studies switchi...

Simplex type algorithms perform successive pivoting operations (or iterations) in order to reach the optimal solution. The choice of the pivot element at each iteration is one of the most critical step in simplex type algorithms. The flexibility of the entering and leaving variable selection allows to develop various pivoting rules. In this paper, we have proposed some of the most well-known pi...

The validity of applying paraphrase rules depends on the domain of the text that they are being applied to. We develop a novel method for extracting domainspecific paraphrases. We adapt the bilingual pivoting paraphrase method to bias the training data to be more like our target domain of biology. Our best model results in higher precision while retaining complete recall, giving a 10% relative ...

Almost block diagonal linear systems of equations can be exemplified by two modules. This makes it possible to construct all sequential forms of band and/or block elimination methods, six old and fourteen new. It allows easy assessment of the methods on the basis of their operation counts, storage needs, and admissibility of partial pivoting. It unveils a robust partial pivoting strategylocal p...

An object-oriented Matlab system is described that extends the capabilities of Chebfun to smooth functions of two variables defined on rectangles. Functions are approximated to essentially machine precision by using iterative Gaussian elimination with complete pivoting to form “chebfun2” objects representing low rank approximations. Operations such as integration, differentiation, function eval...