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SuanShu Numerical Library
SuanShu is a Java math library. It is open-source under Apache License 2.0 available iGitHub SuanShu is a large collection of Java classes for basic numerical analysis, statistics, and optimization. It implements a parallel version of the adaptive strassen's algorithm for fast matrix multiplication. SuanShu has been quoted and used in a number of academic works. Features * linear algebra * root finding * curve fitting and interpolation * unconstrained and constrained optimization * statistical analysis * linear regression * probability distributions and random number generation * ordinary and partial differential equation solvers License terms SuanShu is released under the terms of the Apache License 2.0 Examples of usage The following code shows the object-oriented design of the library (in contrast to the traditional procedural design of many other FORTRAN and C numerical libraries) by a simple example of minimization. LogGamma logGamma = new LogGamma(); // the log-ga ... [...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 de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Math
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apache License 2
The Apache () are a group of culturally related Native American tribes in the Southwestern United States, which include the Chiricahua, Jicarilla, Lipan, Mescalero, Mimbreño, Ndendahe (Bedonkohe or Mogollon and Nednhi or Carrizaleño and Janero), Salinero, Plains (Kataka or Semat or " Kiowa-Apache") and Western Apache ( Aravaipa, Pinaleño, Coyotero, Tonto). Distant cousins of the Apache are the Navajo, with whom they share the Southern Athabaskan languages. There are Apache communities in Oklahoma and Texas, and reservations in Arizona and New Mexico. Apache people have moved throughout the United States and elsewhere, including urban centers. The Apache Nations are politically autonomous, speak several different languages, and have distinct cultures. Historically, the Apache homelands have consisted of high mountains, sheltered and watered valleys, deep canyons, deserts, and the southern Great Plains, including areas in what is now Eastern Arizona, Norther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Recipes
''Numerical Recipes'' is the generic title of a series of books on algorithms and numerical analysis by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. In various editions, the books have been in print since 1986. The most recent edition was published in 2007. Overview The ''Numerical Recipes'' books cover a range of topics that include both classical numerical analysis (interpolation, integration, linear algebra, differential equations, and so on), signal processing ( Fourier methods, filtering), statistical treatment of data, and a few topics in machine learning (hidden Markov model, support vector machines). The writing style is accessible and has an informal tone. The emphasis is on understanding the underlying basics of techniques, not on the refinements that may, in practice, be needed to achieve optimal performance and reliability. Few results are proved with any degree of rigor, although the ideas behind proofs are often sketched, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second-order Cone Programming
A second-order cone program (SOCP) is a convex optimization problem of the form :minimize \ f^T x \ :subject to ::\lVert A_i x + b_i \rVert_2 \leq c_i^T x + d_i,\quad i = 1,\dots,m ::Fx = g \ where the problem parameters are f \in \mathbb^n, \ A_i \in \mathbb^, \ b_i \in \mathbb^, \ c_i \in \mathbb^n, \ d_i \in \mathbb, \ F \in \mathbb^, and g \in \mathbb^p. x\in\mathbb^n is the optimization variable. \lVert x \rVert_2 is the Euclidean norm and ^T indicates transpose. The "second-order cone" in SOCP arises from the constraints, which are equivalent to requiring the affine function (A x + b, c^T x + d) to lie in the second-order cone in \mathbb^. SOCPs can be solved by interior point methods and in general, can be solved more efficiently than semidefinite programming (SDP) problems. Some engineering applications of SOCP include filter design, antenna array weight design, truss design, and grasping force optimization in robotics. Applications in quantitative finance include p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semidefinite Programming
Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron. Semidefinite programming is a relatively new field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be modeled or approximated as semidefinite programming problems. In automatic control theory, SDPs are used in the context of linear matrix inequalities. SDPs are in fact a special case of cone programming and can be efficiently solved by interior point methods. All linear programs and (convex) quadratic programs can be expressed as SDPs, and via hierarchies of SDPs the solutions of polynomial optimization problems can be approximated. Semidefinite programming has been ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Quadratic Programming
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable. SQP methods solve a sequence of optimization subproblems, each of which optimizes a quadratic model of the objective subject to a linearization of the constraints. If the problem is unconstrained, then the method reduces to Newton's method for finding a point where the gradient of the objective vanishes. If the problem has only equality constraints, then the method is equivalent to applying Newton's method to the first-order optimality conditions, or Karush–Kuhn–Tucker conditions, of the problem. Algorithm basics Consider a nonlinear programming problem of the form: :\begin \min\limits_ & f(x) \\ \mbox & b(x) \ge 0 \\ & c(x) = 0. \end The Lagrangian for this problem is :\mathcal(x,\lambda,\sigma) = f(x) - \lambda b(x) - \sigma c(x), w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interior-point Method
Interior-point methods (also referred to as barrier methods or IPMs) are a certain class of algorithms that solve linear and nonlinear convex optimization problems. An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967 and reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, which runs in provably polynomial time and is also very efficient in practice. It enabled solutions of linear programming problems that were beyond the capabilities of the simplex method. Contrary to the simplex method, it reaches a best solution by traversing the interior of the feasible region. The method can be generalized to convex programming based on a self-concordant barrier function used to encode the convex set. Any convex optimization problem can be transformed into minimizing (or maximizing) a linear function over a convex set by converting to the epigraph form. The idea of encodi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Libraries
{{disambig ...
Numerical may refer to: * Number * Numerical digit * Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (programming Language) Libraries
Java (; id, Jawa, ; jv, ꦗꦮ; su, ) is one of the Greater Sunda Islands in Indonesia. It is bordered by the Indian Ocean to the south and the Java Sea to the north. With a population of 151.6 million people, Java is the world's most populous island, home to approximately 56% of the Indonesian population. Indonesia's capital city, Jakarta, is on Java's northwestern coast. Many of the best known events in Indonesian history took place on Java. It was the centre of powerful Hindu-Buddhist empires, the Islamic sultanates, and the core of the colonial Dutch East Indies. Java was also the center of the Indonesian struggle for independence during the 1930s and 1940s. Java dominates Indonesia politically, economically and culturally. Four of Indonesia's eight UNESCO world heritage sites are located in Java: Ujung Kulon National Park, Borobudur Temple, Prambanan Temple, and Sangiran Early Man Site. Formed by volcanic eruptions due to geologic subduction of the Aust ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public-domain Software With Source Code
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 waived, or may be inapplicable. Because those rights have expired, anyone can legally use or reference those works without permission. As examples, the works of William Shakespeare, Ludwig van Beethoven, 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 Newtonian physics, cooking recipes,Copyright Protec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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