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Lis (linear Algebra Library)
Lis (Library of Iterative Solvers for linear systems, pronounced is is a scalable parallel software library for solving discretized linear equations and eigenvalue problems that mainly arise in the numerical solution of partial differential equations by using iterative methods. Although it is designed for parallel computers, the library can be used without being conscious of parallel processing. Features Lis provides facilities for: * Automatic program configuration * NUMA aware hybrid implementation with MPI and OpenMP * Exchangeable dense and sparse matrix storage formats * Basic linear algebra operations for dense and sparse matrices * Parallel iterative methods for linear equations and eigenvalue problems * Parallel preconditioners for iterative methods * Quadruple precision floating point operations * Performance analysis * Command-line interface to solvers and benchmarks Example A C program to solve the linear equation Ax=b is written as follows: #include #in ... [...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] |
Sparse Matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Numerical Libraries
This is a list of numerical libraries, which are libraries used in software development for performing numerical calculations. It is not a complete listing but is instead a list of numerical libraries with articles on Wikipedia, with few exceptions. The choice of a typical library depends on a range of requirements such as: desired features (e.g. large dimensional linear algebra, parallel computation, partial differential equations), licensing, readability of API, portability or platform/compiler dependence (e.g. Linux, Windows, Visual C++, GCC), performance, ease-of-use, continued support from developers, standard compliance, specialized optimization in code for specific application scenarios or even the size of the code-base to be installed. Multi-language C C++ Delphi * ALGLIB - an open source numerical analysis library. .NET Framework languages C#, F#, VB.NET and PowerShell Fortran Java * SuanShu is an open-source Java math library. It supports numerical anal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
OpenModelica
OpenModelica is a free and open source environment based on the Modelica modeling language for modeling, simulating, optimizing and analyzing complex dynamic systems. This software is actively developed by Open Source Modelica Consortium, a non-profit, non-governmental organization. The Open Source Modelica Consortium is run as a project oRISE SICS East AB in collaboration with Linköping University. OpenModelica is used in academic and industrial environments. Industrial applications include the use of OpenModelica along with proprietary software in the fields of power plant optimization, automotive and water treatment. Tools and Applications OpenModelica Compiler (OMC)OpenModelica Compiler (OMC) is a |
Gerris (software)
Gerris is computer software in the field of computational fluid dynamics (CFD). Gerris was released as free and open-source software, subject to the requirements of the GNU General Public License (GPL), version 2 or any later. Scope ''Gerris'' solves the Navier–Stokes equations in 2 or 3 dimensions, allowing to model industrial fluids (aerodynamics, internal flows, etc.) or for instance, the mechanics of droplets, thanks to an accurate formulation of multiphase flows (including surface tension). Actually, the latter field of study is the reason why the software shares the same name as the insect genus. ''Gerris'' also provides features relevant to geophysical flows: # ocean tide # tsunamis # river flow # eddies in the ocean # sea state (surface waves) Flow types #1 to #3 were studied using the shallow-water solver included in ''Gerris'', case #4 brings in the primitives equations and application #5 relies on the ''spectral'' equations for generation/propagation/dissipatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harwell-Boeing File Format
The Harwell-Boeing file format (also known as HB format ) is a file format designed to store information used to describe sparse matrices In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse b .... References See also * Matrix Market exchange formats External links HB Files Harwell Boeing Sparse Matrix File Formata detailed description of the HB format Computer file formats {{storage-software-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Market Exchange Formats
The Matrix Market exchange formats are a set of human readable, ASCII-based file formats designed to facilitate the exchange of matrix data. The file formats were designed and adopted for the Matrix Market, a NIST repository for test data for use in comparative studies of algorithms for numerical linear algebra. See also * Harwell-Boeing file format The Harwell-Boeing file format (also known as HB format ) is a file format designed to store information used to describe sparse matrices In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which mos ... References External links Matrix Market exchange formats {{software-stub Computer file formats ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multigrid Method
In numerical analysis, a multigrid method (MG method) is an algorithm for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in problems exhibiting multiple scales of behavior. For example, many basic relaxation methods exhibit different rates of convergence for short- and long-wavelength components, suggesting these different scales be treated differently, as in a Fourier analysis approach to multigrid. MG methods can be used as solvers as well as preconditioners. The main idea of multigrid is to accelerate the convergence of a basic iterative method (known as relaxation, which generally reduces short-wavelength error) by a ''global'' correction of the fine grid solution approximation from time to time, accomplished by solving a coarse problem. The coarse problem, while cheaper to solve, is similar to the fine grid problem in that it also has short- and long-wavelength error ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Command-line Interface
A command-line interpreter or command-line processor uses a command-line interface (CLI) to receive commands from a user in the form of lines of text. This provides a means of setting parameters for the environment, invoking executables and providing information to them as to what actions they are to perform. In some cases the invocation is conditional based on conditions established by the user or previous executables. Such access was first provided by computer terminals starting in the mid-1960s. This provided an interactive environment not available with punched cards or other input methods. Today, many users rely upon graphical user interfaces and menu-driven interactions. However, some programming and maintenance tasks may not have a graphical user interface and use a command line. Alternatives to the command-line interface include text-based user interface menus (for example, IBM AIX SMIT), keyboard shortcuts, and various desktop metaphors centered on the pointer (usual ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Profiling (computer Programming)
In software engineering, profiling ("program profiling", "software profiling") is a form of dynamic program analysis that measures, for example, the space (memory) or time complexity of a program, the usage of particular instructions, or the frequency and duration of function calls. Most commonly, profiling information serves to aid program optimization, and more specifically, performance engineering. Profiling is achieved by instrumenting either the program source code or its binary executable form using a tool called a ''profiler'' (or ''code profiler''). Profilers may use a number of different techniques, such as event-based, statistical, instrumented, and simulation methods. Gathering program events Profilers use a wide variety of techniques to collect data, including hardware interrupts, code instrumentation, instruction set simulation, operating system hooks, and performance counters. Use of profilers The output of a profiler may be: * A statistical ''sum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating Point
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadruple-precision Floating-point Format
In computing, quadruple precision (or quad precision) is a binary floating point–based computer number format that occupies 16 bytes (128 bits) with precision at least twice the 53-bit double precision. This 128-bit quadruple precision is designed not only for applications requiring results in higher than double precision, but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables. William Kahan, primary architect of the original IEEE-754 floating point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format ... That kind of gradual evolution towards wider precision was already in view when IEEE Standard 754 for Floating-Poi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
