Concepts inScalable matrix inversion using MapReduce
Invertible matrix
In linear algebra an n-by-n (square) matrix A is called invertible (some authors use nonsingular or nondegenerate) if there exists an n-by-n matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A.
more from Wikipedia
MapReduce
MapReduce is a programming model for processing large data sets, and the name of an implementation of the model by Google. MapReduce is typically used to do distributed computing on clusters of computers. The model is inspired by the map and reduce functions commonly used in functional programming, although their purpose in the MapReduce framework is not the same as their original forms. MapReduce libraries have been written in many programming languages.
more from Wikipedia
Scalability
In electronics scalability is the ability of a system, network, or process, to handle growing amount of work in a capable manner or its ability to be enlarged to accommodate that growth. For example, it can refer to the capability of a system to increase total throughput under an increased load when resources (typically hardware) are added.
more from Wikipedia
LU decomposition
In linear algebra, LU decomposition (also called LU factorization) factorizes a matrix as the product of a lower triangular matrix and an upper triangular matrix. The product sometimes includes a permutation matrix as well. LU decomposition is a key step in several fundamental numerical algorithms in linear algebra such as solving a system of linear equations, inverting a matrix, or computing the determinant of a matrix. It can be viewed as the matrix form of Gaussian elimination.
more from Wikipedia
ScaLAPACK
The ScaLAPACK (or Scalable LAPACK) library includes a subset of LAPACK routines redesigned for distributed memory MIMD parallel computers. It is currently written in a Single-Program-Multiple-Data style using explicit message passing for interprocessor communication. It assumes matrices are laid out in a two-dimensional block cyclic decomposition. ScaLAPACK is designed for heterogeneous computing and is portable on any computer that supports MPI or PVM.
more from Wikipedia
Amazon Elastic Compute Cloud
Amazon Elastic Compute Cloud (EC2) is a central part of Amazon. com's cloud computing platform, Amazon Web Services (AWS). EC2 allows users to rent virtual computers on which to run their own computer applications. EC2 allows scalable deployment of applications by providing a Web service through which a user can boot an Amazon Machine Image to create a virtual machine, which Amazon calls an "instance", containing any software desired.
more from Wikipedia
Computational science
Computational science (or scientific computing) is the subfield of computer science concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems. In practical use, it is typically the application of computer simulation and other forms of computation from theoretical computer science to problems in various scientific disciplines.
more from Wikipedia
Apache Hadoop
Apache Hadoop is a software framework that supports data-intensive distributed applications under a free license. It enables applications to work with thousands of computational independent computers and petabytes of data. Hadoop was derived from Google's MapReduce and Google File System (GFS) papers. Hadoop is a top-level Apache project being built and used by a global community of contributors, written in the Java programming language.
more from Wikipedia