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LINPACK Benchmarks
The LINPACK Benchmarks are a measure of a system's floating-point computing power. Introduced by Jack Dongarra, they measure how fast a computer solves a dense ''n'' by ''n'' system of linear equations ''Ax'' = ''b'', which is a common task in engineering. The latest version of these benchmarks is used to build the TOP500 list, ranking the world's most powerful supercomputers. The aim is to approximate how fast a computer will perform when solving real problems. It is a simplification, since no single computational task can reflect the overall performance of a computer system. Nevertheless, the LINPACK benchmark performance can provide a good correction over the peak performance provided by the manufacturer. The peak performance is the maximal theoretical performance a computer can achieve, calculated as the machine's frequency, in cycles per second, times the number of operations per cycle it can perform. The actual performance will always be lower than the peak perfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jack Dongarra
Jack Joseph Dongarra (born July 18, 1950) is an American computer scientist and mathematician. He is the American University Distinguished Professor of Computer Science in the Electrical Engineering and Computer Science Department at the University of Tennessee. He holds the position of a Distinguished Research Staff member in the Computer Science and Mathematics Division at Oak Ridge National Laboratory, Turing Fellowship in the School of Mathematics at the University of Manchester, and is an adjunct professor in the Computer Science Department at Rice University. He served as a faculty fellow at the Texas A&M University Institute for Advanced Study (2014–2018). Dongarra is the founding director of the Innovative Computing Laboratory at the University of Tennessee. Education Dongarra received a BSc degree in Mathematics from Chicago State University in 1972 and a MSc degree in Computer Science from the Illinois Institute of Technology in 1973. In 1980, he received PhD in Ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strassen Algorithm
In linear algebra, the Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix multiplication algorithm for large matrices, with a better asymptotic complexity, although the naive algorithm is often better for smaller matrices. The Strassen algorithm is slower than the fastest known algorithms for extremely large matrices, but such galactic algorithms are not useful in practice, as they are much slower for matrices of practical size. For small matrices even faster algorithms exist. Strassen's algorithm works for any ring, such as plus/multiply, but not all semirings, such as min-plus or boolean algebra, where the naive algorithm still works, and so called combinatorial matrix multiplication. History Volker Strassen first published this algorithm in 1969 and thereby proved that the n^3 general matrix multiplication algorithm wasn't optimal. The Strassen algorithm's publication resulted in more resear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dense Linear System
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically, density is defined as mass divided by volume: : \rho = \frac where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate – this quantity is more specifically called specific weight. For a pure substance the density has the same numerical value as its mass concentration (chemistry), mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium and iridium are the densest known elements at standard conditions for temperature and pressure. To simplify comparisons of dens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Broadcasting (computing)
In computer networking, telecommunication and information theory, broadcasting is a method of transferring a message to all recipients simultaneously. Broadcasting can be performed as a high-level operation in a program, for example, broadcasting in Message Passing Interface, or it may be a low-level networking operation, for example broadcasting on Ethernet. All-to-all communication is a computer communication method in which each sender transmits messages to all receivers within a group. In networking this can be accomplished using broadcast or multicast. This is in contrast with the point-to-point method in which each sender communicates with one receiver. Addressing methods There are four principal addressing methods in the Internet Protocol: Overview In computer networking, broadcasting refers to transmitting a packet that will be received by every device on the network. In practice, the scope of the broadcast is limited to a broadcast domain. Broadcasting is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Look-ahead (LU Factorization)
Lookahead or Look Ahead may refer to: * A parameter of some combinatorial search algorithms, describing how deeply the graph representing the problem is explored * A parameter of some parsing algorithms; the maximum number of tokens that a parser can use to decide which rule to use * In dynamic range compression, a signal processing design to avoid compromise between slow attack rates that produce smooth-sounding gain changes, and fast attack rates capable of catching transients * Look-ahead (backtracking), a subprocedure that attempts to predict the effects of choosing a branching variable to evaluate or one of its values * Lookahead carry unit, a logical unit in digital circuit design used to decrease calculation time in adder units * Look Ahead, a charitable housing association in London * In regular expressions, an assertion to match characters after the current position Education *''Look Ahead'', 1990s English as a foreign language multimedia classroom project by BBC Englis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LU Factorization
In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix. The LU decomposition was introduced by the Polish mathematician Tadeusz Banachiewicz in 1938. Definitions Let ''A'' be a square matrix. An LU factorization refers to the factorization of ''A'', with proper row and/or column orderings or permutations, into two factors – a lower triangular matrix ''L'' and an upper triangular matrix ''U'': : A = LU. In the lower triangular matrix all elements above the diagonal are zero, in the upper triangular matrix, all the el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
BLAS
Basic Linear Algebra Subprograms (BLAS) is a specification that prescribes a set of low-level routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. They are the ''de facto'' standard low-level routines for linear algebra libraries; the routines have bindings for both C ("CBLAS interface") and Fortran ("BLAS interface"). Although the BLAS specification is general, BLAS implementations are often optimized for speed on a particular machine, so using them can bring substantial performance benefits. BLAS implementations will take advantage of special floating point hardware such as vector registers or SIMD instructions. It originated as a Fortran library in 1979* and its interface was standardized by the BLAS Technical (BLAST) Forum, whose latest BLAS report can be found on the netlib website. This Fortran library is known as the ''reference implementation'' (sometimes co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (programming Language)
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers ''write once, run anywhere'' ( WORA), meaning that compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax of Java is similar to C and C++, but has fewer low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as reflection and runtime code modification) that are typically not available in traditional compiled languages. , Java was one of the most popular programming languages in use according to GitHub, particularly for client–server web applications, with a reported 9 million developers. Java was originally developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Implementation
Implementation is the realization of an application, or execution of a plan, idea, model, design, specification, standard, algorithm, or policy. Industry-specific definitions Computer science In computer science, an implementation is a realization of a technical specification or algorithm as a program, software component, or other computer system through computer programming and deployment. Many implementations may exist for a given specification or standard. For example, web browsers contain implementations of World Wide Web Consortium-recommended specifications, and software development tools contain implementations of programming languages. A special case occurs in object-oriented programming, when a concrete class implements an interface; in this case the concrete class is an ''implementation'' of the interface and it includes methods which are ''implementations'' of those methods specified by the interface. Information technology In the information technology during ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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