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JAMA (numerical Linear Algebra Library)
JAMA is a software library for performing numerical linear algebra tasks created at National Institute of Standards and Technology in 1998 similar in functionality to LAPACK. Functionality The main capabilities provided by JAMA are: * Eigensystem solving * LU decomposition * Singular value decomposition * QR decomposition * Cholesky decomposition Versions exist for both C++ and the Java programming language. The C++ version uses the Template Numerical Toolkit for lower-level operations. The Java version provides the lower-level operations itself. History As work of US governmental organization the algorithm and source code have been released to the public domain around 1998. on math.nist.gov JAMA has had little development since the year 2000, with only the occasional bug fix being ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical science laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement. From 1901 to 1988, the agency was named the National Bureau of Standards. History Background The Articles of Confederation, ratified by the colonies in 1781, provided: The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective states—fixing the standards of weights and measures throughout the United States. Article 1, section 8, of the Constitution of the United States, ratified in 1789, granted these powers to the new Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
QR Decomposition
In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix ''A'' into a product ''A'' = ''QR'' of an orthonormal matrix ''Q'' and an upper triangular matrix ''R''. QR decomposition is often used to solve the linear least squares (LLS) problem and is the basis for a particular eigenvalue algorithm, the QR algorithm. Cases and definitions Square matrix Any real square matrix ''A'' may be decomposed as : A = QR, where ''Q'' is an orthogonal matrix (its columns are orthogonal unit vectors meaning and ''R'' is an upper triangular matrix (also called right triangular matrix). If ''A'' is invertible, then the factorization is unique if we require the diagonal elements of ''R'' to be positive. If instead ''A'' is a complex square matrix, then there is a decomposition ''A'' = ''QR'' where ''Q'' is a unitary matrix (so the conjugate transpose If ''A'' has ''n'' linearly independent columns, then the first ''n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Software
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt to find approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences like economics, medicine, business and even the arts. Current growth in computing power has enabled the use of more complex numerical analysis, providing detailed and realistic mathematical models in science and engineering. Examples of numerical analysis include: ordinary differential equations as found in celestial mechanics (predicting the motions of planets, stars and galaxies), numerical linear algebra in data analysis, and stochastic differential equations and Markov chains for simulati ... [...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 OCaml * OCaml programming language has support for array programming ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public Domain
The public domain (PD) consists of all the creative work to which no Exclusive exclusive intellectual property rights apply. Those rights may have expired, been forfeited, expressly Waiver, waived, or may be inapplicable. Because no one holds the exclusive rights, anyone can legally use or reference those works without permission. As examples, the works of William Shakespeare, Ludwig van Beethoven, Miguel de Cervantes, Zoroaster, Lao Zi, Confucius, Aristotle, L. Frank Baum, Leonardo da Vinci and Georges Méliès are in the public domain either by virtue of their having been created before copyright existed, or by their copyright term having expired. Some works are not covered by a country's copyright laws, and are therefore in the public domain; for example, in the United States, items excluded from copyright include the formulae of Classical mechanics, Newtonian physics and cooking recipes. Other works are actively dedicated by their authors to the public domain (see waiver) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Source Code
In computing, source code, or simply code or source, is a plain text computer program written in a programming language. A programmer writes the human readable source code to control the behavior of a computer. Since a computer, at base, only understands machine code, source code must be Translator (computing), translated before a computer can Execution (computing), execute it. The translation process can be implemented three ways. Source code can be converted into machine code by a compiler or an assembler (computing), assembler. The resulting executable is machine code ready for the computer. Alternatively, source code can be executed without conversion via an interpreter (computing), interpreter. An interpreter loads the source code into memory. It simultaneously translates and executes each statement (computer science), statement. A method that combines compilation and interpretation is to first produce bytecode. Bytecode is an intermediate representation of source code tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Template Numerical Toolkit
{{Portal, Free and open-source software The Template Numerical Toolkit (or TNT) is a software library for manipulating vectors and matrices in C++ created by the U.S. National Institute of Standards and Technology. TNT provides the fundamental linear algebra operations (for example, matrix multiplication). TNT is analogous to the BLAS library used by LAPACK. Higher level algorithms, such as LU decomposition and singular value decomposition, are provided by JAMA, also developed at NIST, which uses TNT. The major features of TNT are: * All classes are template classes and therefore work with float, double, or other user-defined number types. * Matrices can be stored in row-major order or column-major order for Fortran compatibility. * The library is simply a collection of header files, and therefore does not need to be independently compiled. * Some support for sparse matrix storage is provided. * The source code is in the public domain. TNT is mature, and NIST classifies i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java Programming Language
Java is a high-level, general-purpose, memory-safe, object-oriented programming language. It is 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 gained popularity shortly after its release, and has been a popular programming language since then. Java was the third most popular programming language in according to GitHub. Although still widely popular, there has been a gradual decline in use of Java in recent years with other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cholesky Decomposition
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced ) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices, and posthumously published in 1924. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations. Statement The Cholesky decomposition of a Hermitian positive-definite matrix , is a decomposition of the form \mathbf = \mathbf^, where is a lower triangular matrix with real and positive diagonal entries, and * denotes the conjugate transpose of . Every Hermitian positive-definite matrix (and thus also every real-valued symmetric positive-definite matrix) has a unique Cholesky decomposition. The converse holds trivially: if can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Value Decomposition
In linear algebra, the singular value decomposition (SVD) is a Matrix decomposition, factorization of a real number, real or complex number, complex matrix (mathematics), matrix into a rotation, followed by a rescaling followed by another rotation. It generalizes the eigendecomposition of a square normal matrix with an orthonormal eigenbasis to any matrix. It is related to the polar decomposition#Matrix polar decomposition, polar decomposition. Specifically, the singular value decomposition of an m \times n complex matrix is a factorization of the form \mathbf = \mathbf, where is an complex unitary matrix, \mathbf \Sigma is an m \times n rectangular diagonal matrix with non-negative real numbers on the diagonal, is an n \times n complex unitary matrix, and \mathbf V^* is the conjugate transpose of . Such decomposition always exists for any complex matrix. If is real, then and can be guaranteed to be real orthogonal matrix, orthogonal matrices; in such contexts, the SVD ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross-platform
Within computing, cross-platform software (also called multi-platform software, platform-agnostic software, or platform-independent software) is computer software that is designed to work in several Computing platform, computing platforms. Some cross-platform software requires a separate build for each platform, but some can be directly run on any platform without special preparation, being written in an interpreted language or compiled to portable bytecode for which the Interpreter (computing), interpreters or run-time packages are common or standard components of all supported platforms. For example, a cross-platform application software, application may run on Linux, macOS and Microsoft Windows. Cross-platform software may run on many platforms, or as few as two. Some frameworks for cross-platform development are Codename One, ArkUI-X, Kivy (framework), Kivy, Qt (software), Qt, GTK, Flutter (software), Flutter, NativeScript, Xamarin, Apache Cordova, Ionic (mobile app framework ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LU Decomposition
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 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. 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. It is also sometimes referred to as LR decomposition (factors into left and right triangular matrices). The LU decomposition was introduced by the Polish astronomer Tadeusz Banachiewicz in 1938, who first wrote product equation LU=A=h^Tg (The last form in his alternate yet equivalent matrix notation appears as g\times h. ) Definitions Let ''A'' be a square matrix. An LU factorization refers to expression of ''A'' into product of two facto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
