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Projective Method
Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice. Denoting by n the number of variables, ''m'' the number of inequality constraints, and L the number of bits of input to the algorithm, Karmarkar's algorithm requires O(m^ n^ L) operations on O(L)-digit numbers, as compared to O(n^3(n+m) L) such operations for the ellipsoid algorithm. In "square" problems, when ''m'' is in O(''n''), Karmarkar's algorithm requires O(n^ L) operations on O(L)-digit numbers, as compared to O(n^4 L) such operations for the ellipsoid algorithm. The runtime of Karmarkar's algorithm is thus : O(n^ L^2 \cdot \log L \cdot \log \log L), using FFT-based multiplication (see Big O notation). Karmarkar's algorithm falls within the class of interior-point methods: th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanford University
Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth List of governors of California, governor of and then-incumbent List of United States senators from California, United States senator representing California) and his wife, Jane Stanford, Jane, in memory of their only child, Leland Stanford Jr., Leland Jr. The university admitted its first students in 1891, opening as a Mixed-sex education, coeducational and non-denominational institution. It struggled financially after Leland died in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, university Provost (education), provost Frederick Terman inspired an entrepreneurship, entrepreneurial culture to build a self-sufficient local industry (later Silicon Valley). In 1951, Stanfor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Processor
In computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called ''vectors''. This is in contrast to scalar processors, whose instructions operate on single data items only, and in contrast to some of those same scalar processors having additional single instruction, multiple data (SIMD) or SIMD within a register (SWAR) Arithmetic Units. Vector processors can greatly improve performance on certain workloads, notably numerical simulation, compression and similar tasks. Vector processing techniques also operate in video-game console hardware and in graphics accelerators. Vector machines appeared in the early 1970s and dominated supercomputer design through the 1970s into the 1990s, notably the various Cray platforms. The rapid fall in the price-to-performance ratio of conventional microprocessor de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barrier Function
In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value increases to infinity as its argument approaches the boundary of the feasible region of an optimization problem. Such functions are used to replace inequality constraints by a penalizing term in the objective function that is easier to handle. A barrier function is also called an interior penalty function, as it is a penalty function that forces the solution to remain within the interior of the feasible region. The two most common types of barrier functions are inverse barrier functions and logarithmic barrier functions. Resumption of interest in logarithmic barrier functions was motivated by their connection with primal-dual interior point methods. Motivation Consider the following constrained optimization problem: :minimize :subject to where is some constant. If one wishes to remove the inequality constraint, the problem can be reformulated as :minimize , :where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projected Newton Barrier Method
Projected is an American rock supergroup consisting of Sevendust members John Connolly and Vinnie Hornsby, Alter Bridge and Creed drummer Scott Phillips, and former Submersed and current Tremonti guitarist Eric Friedman. The band released their album, ''Human'', in June 2012, before falling into inactivity as members returned to their respective bands in late 2012. The band released their second studio album, the double album, '' Ignite My Insanity'', in July 2017. They reconvened in early 2020 and finished recording their third album in July 2020. History The band recorded as a four-piece, with each of the members coming from different bands. John Connolly and Vinnie Hornsby had both played together for many years in the alternative metal band Sevendust, as the guitarist and bassist respectively. Eric Friedman had previously been the guitarist for the now-defunct band Submersed, currently playing with Tremonti (formed with Mark Tremonti and Garrett Whitlock), and Scott ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip Gill
Philip, also Phillip, is a male name derived from the Greek (''Philippos'', lit. "horse-loving" or "fond of horses"), from a compound of (''philos'', "dear", "loved", "loving") and (''hippos'', "horse"). Prominent Philips who popularized the name include kings of Macedonia and one of the apostles of early Christianity. ''Philip'' has many alternative spellings. One derivation often used as a surname is Phillips. The original Greek spelling includes two Ps as seen in Philippides and Philippos, which is possible due to the Greek endings following the two Ps. To end a word with such a double consonant—in Greek or in English—would, however, be incorrect. It has many diminutive (or even hypocoristic) forms including Phil, Philly, Phillie, Lip, and Pip. There are also feminine forms such as Philippine and Philippa. Philip in other languages * Afrikaans: Filip * Albanian: Filip * Amharic: ፊሊጶስ (Filip'os) * Arabic: فيلبس (Fīlibus), فيليبوس (Fīlībūs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Analysis
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] |
Prior Art
Prior art (also known as state of the art or background art) is a concept in patent law used to determine the patentability of an invention, in particular whether an invention meets the novelty and the inventive step or non-obviousness criteria for patentability. In most systems of patent law, prior art is generally defined as anything that is made available, or disclosed, to the public that might be relevant to a patent's claim before the effective filing date of a patent application for an invention. However, notable differences exist in how prior art is specifically defined under different national, regional, and international patent systems. The prior art is evaluated by patent offices as part of the patent granting process in what is called "substantive examination" of a patent application in order to determine whether an invention claimed in the patent application meets the novelty and inventive step or non-obviousness criteria for patentability. It may also be considered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RSA (algorithm)
The RSA (Rivest–Shamir–Adleman) cryptosystem is a public-key cryptosystem, one of the oldest widely used for secure data transmission. The initialism "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government Communications Headquarters (GCHQ), the British signals intelligence agency, by the English mathematician Clifford Cocks. That system was declassified in 1997. In a public-key cryptosystem, the encryption key is public and distinct from the decryption key, which is kept secret (private). An RSA user creates and publishes a public key based on two large prime numbers, along with an auxiliary value. The prime numbers are kept secret. Messages can be encrypted by anyone via the public key, but can only be decrypted by someone who knows the private key. The security of RSA relies on the practical difficulty of factoring the product of two ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ronald Rivest
Ronald Linn Rivest (; born May 6, 1947) is an American cryptographer and computer scientist whose work has spanned the fields of algorithms and combinatorics, cryptography, machine learning, and election integrity. He is an Institute Professor at the Massachusetts Institute of Technology (MIT), and a member of MIT's Department of Electrical Engineering and Computer Science and its Computer Science and Artificial Intelligence Laboratory. Along with Adi Shamir and Len Adleman, Rivest is one of the inventors of the RSA algorithm. He is also the inventor of the symmetric key encryption algorithms RC2, RC4, and RC5, and co-inventor of RC6. (''RC'' stands for "Rivest Cipher".) He also devised the MD2, MD4, MD5 and MD6 cryptographic hash functions. Education Rivest earned a bachelor's degree in mathematics from Yale University in 1969, and a Ph.D. degree in computer science from Stanford University in 1974 for research supervised by Robert W. Floyd. Career At MIT, Riv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The New York Times
''The New York Times'' (''NYT'') is an American daily newspaper based in New York City. ''The New York Times'' covers domestic, national, and international news, and publishes opinion pieces, investigative reports, and reviews. As one of the longest-running newspapers in the United States, the ''Times'' serves as one of the country's Newspaper of record, newspapers of record. , ''The New York Times'' had 9.13 million total and 8.83 million online subscribers, both by significant margins the List of newspapers in the United States, highest numbers for any newspaper in the United States; the total also included 296,330 print subscribers, making the ''Times'' the second-largest newspaper by print circulation in the United States, following ''The Wall Street Journal'', also based in New York City. ''The New York Times'' is published by the New York Times Company; since 1896, the company has been chaired by the Ochs-Sulzberger family, whose current chairman and the paper's publ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Patent
A software patent is a patent on a piece of software, such as a computer program, library, user interface, or algorithm. The validity of these patents can be difficult to evaluate, as software is often at once a product of engineering, something typically eligible for patents, and an abstract concept, which is typically not. This gray area, along with the difficulty of patent evaluation for intangible, technical works such as libraries and algorithms, makes software patents a frequent subject of controversy and litigation. Different jurisdictions have radically different policies concerning software patents, including a blanket ban, no restrictions, or attempts to distinguish between purely mathematical constructs and "embodiments" of these constructs. For example, an algorithm itself may be judged unpatentable, but its use in software judged patentable. Background A patent is a set of exclusionary rights granted by a state to a patent holder for a limited period of time, usual ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
