LU reduction is an algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

 related to LU decomposition

LU decomposition

In linear algebra, LU decomposition is a matrix decomposition which writes a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. This decomposition is used in numerical analysis to solve systems of linear...

. This term is usually used in the context of super computing and highly parallel computing

Parallel computing

Parallel computing is a form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently . There are several different forms of parallel computing: bit-level,...

. In this context it is used as a benchmarking

Benchmarking

Benchmarking is the process of comparing one's business processes and performance metrics to industry bests and/or best practices from other industries. Dimensions typically measured are quality, time and cost...

algorithm, i.e. to provide a comparative measurement of speed for different computers. LU reduction is a special parallelized version of an LU decomposition algorithm, an example can be found in (Guitart 2001). The parallelized version usually distributes the work for a matrix row to a single processor and synchronizes the result with the whole matrix (Escribano 2000).

Sources

• J. Oliver, J. Guitart, E. Ayguadé, N. Navarro and J. Torres. Strategies for Efficient Exploitation of Loop-level Parallelism in Java. Concurrency and Computation: Practice and Experience(Java Grande 2000 Special Issue), Vol.13 (8-9), pp. 663–680. ISSN 1532-0634, July 2001, http://www.bsc.es/media/396.pdf, last retrieved on Sept. 14 2007
• J. Guitart, X. Martorell, J. Torres, and E. Ayguadé, Improving Java Multithreading Facilities: the Java Nanos Environment, Research Report UPC-DAC-2001-8, Computer Architecture Department, Technical University of Catalonia, March 2001, http://elio.ac.upc.edu/~dacsecre/reports/2001/8/contents.ps.Z.
• Arturo González-Escribano, Arjan J. C. van Gemund, Valentín Cardeñoso-Payo et al., Measuring the Performance Impact of SP-Restricted Programming in Shared-Memory Machines, In Vector and Parallel Processing — VECPAR 2000, Springer Verlag, pp. 128–141, ISBN 978-3-540-41999-0, 2000, http://www.infor.uva.es/~arturo/Ftp/p-vecpar2000lncs.ps.gz