|
Cannon's Algorithm
In computer science, Cannon's algorithm is a distributed algorithm for matrix multiplication for two-dimensional meshes first described in 1969 by Lynn Elliot Cannon.Gupta, H.; Sadayappan, P.: Communication Efficient Matrix-Multiplication on Hypercubes dbpubs.stanford.edu It is especially suitable for computers laid out in an ''N'' × ''N'' mesh. www.phy.ornl.gov While Cannon's algorithm works well in homogeneous 2D grids, extending it to heterogeneous 2D grids has been shown to be difficult.Jean-François Pineau [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributed Algorithm
A distributed algorithm is an algorithm designed to run on computer hardware constructed from interconnected processors. Distributed algorithms are used in different application areas of distributed computing, such as telecommunications, scientific computing, distributed information processing, and real-time process control. Standard problems solved by distributed algorithms include leader election, consensus, distributed search, spanning tree generation, mutual exclusion, and resource allocation. Distributed algorithms are a sub-type of parallel algorithm, typically executed concurrently, with separate parts of the algorithm being run simultaneously on independent processors, and having limited information about what the other parts of the algorithm are doing. One of the major challenges in developing and implementing distributed algorithms is successfully coordinating the behavior of the independent parts of the algorithm in the face of processor failures and unreliable communi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm For Matrix Multiplication
Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms efficient. Applications of matrix multiplication in computational problems are found in many fields including scientific computing and pattern recognition and in seemingly unrelated problems such as counting the paths through a graph. Many different algorithms have been designed for multiplying matrices on different types of hardware, including parallel and distributed systems, where the computational work is spread over multiple processors (perhaps over a network). Directly applying the mathematical definition of matrix multiplication gives an algorithm that takes time on the order of field operations to multiply two matrices over that field ( in big O notation). Better asymptotic bounds on the time required to multiply matrices have been known since the Strassen's algorithm in the 1960s, but the optimal time (that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mesh Networking
A mesh network is a local area network topology in which the infrastructure nodes (i.e. bridges, switches, and other infrastructure devices) connect directly, dynamically and non-hierarchically to as many other nodes as possible and cooperate with one another to efficiently route data to and from clients. This lack of dependency on one node allows for every node to participate in the relay of information. Mesh networks dynamically self-organize and self-configure, which can reduce installation overhead. The ability to self-configure enables dynamic distribution of workloads, particularly in the event a few nodes should fail. This in turn contributes to fault-tolerance and reduced maintenance costs. Mesh topology may be contrasted with conventional star/tree local network topologies in which the bridges/switches are directly linked to only a small subset of other bridges/switches, and the links between these infrastructure neighbours are hierarchical. While star-and-tree topologi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lynn Elliot Cannon
Lynn may refer to: People and fictional characters * Lynn (given name), including a list of people and fictional characters * Lynn (surname) * The Lynns, a 1990s American country music duo consisting of twin sisters Peggy and Patsy Lynn * Lynn (voice actress), Japanese voice actress Places Canada * Lynn Lake, Manitoba, a town and adjacent lake * Lynn, Nova Scotia, a community * Lynn River, Ontario Ireland * Lynn (civil parish), County Westmeath United Kingdom * King's Lynn is a seaport in Norfolk, England, about 98 miles north of London United States * Lynn, Alabama, a town * Lynn, Arkansas, a town * Lynn, Oakland, California, a former settlement * Lynn, Indiana, a town * Lynn, Massachusetts, a city ** Lynn (MBTA station) * Lynn, Nebraska, an unincorporated community * Lynn, Ohio, an unincorporated community * Lynn, Susquehanna County, Pennsylvania, an historic community now part of Springville in Susquehanna County, Pennsylvania Susquehanna County is a count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. ScaLAPACK depends on PBLAS operations in the same way LAPACK LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It al ... depends on BLAS. As of version 2.0 the code base directly includes PBLAS and BLACS and has dropped support for PVM. Examples * Programming with Big Data in R fully utilizes ScaLAPACK and two-dimensional block cyclic de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PLAPACK
LAPACK ("Linear Algebra Package") is a standard software library for numerical linear algebra. It provides routines for solving systems of linear equations and linear least squares, eigenvalue problems, and singular value decomposition. It also includes routines to implement the associated matrix factorizations such as LU, QR, Cholesky and Schur decomposition. LAPACK was originally written in FORTRAN 77, but moved to Fortran 90 in version 3.2 (2008). The routines handle both real and complex matrices in both single and double precision. LAPACK relies on an underlying BLAS implementation to provide efficient and portable computational building blocks for its routines. LAPACK was designed as the successor to the linear equations and linear least-squares routines of LINPACK and the eigenvalue routines of EISPACK. LINPACK, written in the 1970s and 1980s, was designed to run on the then-modern vector computers with shared memory. LAPACK, in contrast, was designed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Systolic Array
In parallel computer architectures, a systolic array is a homogeneous network of tightly coupled data processing units (DPUs) called cells or nodes. Each node or DPU independently computes a partial result as a function of the data received from its upstream neighbours, stores the result within itself and passes it downstream. Systolic arrays were first used in Colossus, which was an early computer used to break German Lorenz ciphers during World War II. Due to the classified nature of Colossus, they were independently invented or rediscovered by H. T. Kung and Charles Leiserson who described arrays for many dense linear algebra computations (matrix product, solving systems of linear equations, LU decomposition, etc.) for banded matrices. Early applications include computing greatest common divisors of integers and polynomials. They are sometimes classified as Multiple instruction, single data, multiple-instruction single-data (MISD) architectures under Flynn's taxonomy, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributed Algorithms
A distributed algorithm is an algorithm designed to run on computer hardware constructed from interconnected processors. Distributed algorithms are used in different application areas of distributed computing, such as telecommunications, scientific computing, distributed information processing, and real-time process control. Standard problems solved by distributed algorithms include leader election, consensus, distributed search, spanning tree generation, mutual exclusion, and resource allocation. Distributed algorithms are a sub-type of parallel algorithm, typically executed concurrently, with separate parts of the algorithm being run simultaneously on independent processors, and having limited information about what the other parts of the algorithm are doing. One of the major challenges in developing and implementing distributed algorithms is successfully coordinating the behavior of the independent parts of the algorithm in the face of processor failures and unreliable communic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Multiplication Algorithms
Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** '' The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchise) * Matrix (mathematics), a rectangular array of numbers, symbols or expressions Matrix (or its plural form matrices) may also refer to: Science and mathematics * Matrix (mathematics), algebraic structure, extension of vector into 2 dimensions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the material in between a eukaryotic organism's cells * Matrix (chemical analysis), the non-analyte components of a sample * Matrix (geology), the fine-grained material in which larger objects are embedded * Matrix (composite), the constituent of a composite material * Hair matrix, produces hair * Nail matrix, part of the nail in anatomy Arts and entertainment Fictional entities * Matrix (comics), two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
