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LINPACK benchmarks

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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 × nsystem of linear equationsAx = 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.

Benchmark (computing)Benchmark (computing)Standardized performance evaluation A graphical demo running as a benchmark of the OGRE engine In computing, a benchmark is the act of running a computer program, a set of programs, or other operations, in order to assess the relative performance of an object, normally by running a number of standard tests and trials against it. The term benchmark is also commonly utilized for the purposes of elaborately designed benchmarking programs themselves.TOP500TOP500Database project devoted to the ranking of computersThe TOP500 project ranks and details the 500 most powerful non-distributed computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year. The first of these updates always coincides with the International Supercomputing Conference in June, and the second is presented at the ACM/IEEE Supercomputing Conference in November.LINPACKLINPACKLINPACK is a software library for performing numerical linear algebra on digital computers. It was written in Fortran by Jack Dongarra, Jim Bunch, Cleve Moler, and Gilbert Stewart, and was intended for use on supercomputers in the 1970s and early 1980s. It has been largely superseded by LAPACK, which runs more efficiently on modern architectures. LINPACK makes use of the BLAS (Basic Linear Algebra Subprograms) libraries for performing basic vector and matrix operations.Computer performanceComputer performanceIn computing, computer performance is the amount of useful work accomplished by a computer system. Outside specific contexts, computer performance is estimated in terms of accuracy, efficiency and speed of executing computer program instructions. When it comes to high computer performance, one or more of the following factors might be involved: Short response time for a given piece of work.High throughput (rate of processing work tasks).Low utilization of computing resources.Double-precision floating-point formatDouble-precision floating-point formatDouble-precision floating-point format (sometimes called FP64 or float64) is a floating-pointnumber format, usually occupying 64 bits in computer memory; it represents a wide range of numeric values by using a floating radix point. Double precision may be chosen when the range or precision of single precision would be insufficient. In the IEEE 754standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985.Floating point operations per secondFloating point operations per secondFloating point operations per second (FLOPS, flops or flop/s) is a measure of computer performance or compute in computing, useful in fields of scientific computations that require floating-point calculations. For such cases, it is a more accurate measure than instructions per second. Floating-point arithmeticFloating-point arithmetic is needed for very large or very small real numbers, or computations that require a large dynamic range.Jack DongarraJack DongarraJack Joseph DongarraFRS (born July 18, 1950) is an American computer scientist and mathematician. He is a University Distinguished Professor Emeritus of Computer Science in the Electrical Engineering and Computer Science Department at the University of Tennessee. He holds the position 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.System of linear equationsSystem of linear equationsIn mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. For example, {3x+2y−z=12x−2y+4z=−2−x+12y−z=0{\displaystyle {\begin{cases}3x+2y-z=1\\2x-2y+4z=-2\\-x+{\frac {1}{2}}y-z=0\end{cases}}} is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied.Floating-point arithmeticFloating-point arithmeticComputer approximation for real numbersAn early electromechanical programmable computer, the Z3, included floating-point arithmetic (replica on display at Deutsches Museum in Munich).In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a significand (a signed sequence of a fixed number of digits in some base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers.LU decompositionLU decompositionType of matrix factorizationIn 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 multiplication and matrix decomposition). The product sometimes includes a permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination.FortranFortranGeneral-purpose programming languageFortran (; formerly FORTRAN) is a third-generation, compiled, imperativeprogramming language designed for numeric computation and scientific computing. Fortran was originally developed by IBM with a reference manual being released in 1956; however, the first compilers only began to produce accurate code two years later.EngineeringEngineeringEngineering is the practice of systematically applying natural science and mathematics to design and improve systems, devices, or processes that solve problems under constraints. It is typically motivated by satisfying human needs, resulting in creations such as bridges, engines, smartphones, pacemakers, the internet, spacecraft, and washing machines.

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