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Charles George Broyden
Charles George Broyden (3 February 1933 – 20 May 2011) was a mathematician who specialized in optimization problems and numerical linear algebra. While a physicist working at English Electric Company from 1961 to 1965, he adapted the Davidon–Fletcher–Powell formula to solving some nonlinear systems of equations that he was working with, leading to his widely cited 1965 paper, "A class of methods for solving nonlinear simultaneous equations". He was a lecturer at UCW Aberystwyth from 1965 to 1967. He later became a senior lecturer at University of Essex from 1967 to 1970, where he independently discovered the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. The BFGS method has then become a key technique in solving nonlinear optimization problems. Moreover, he was among those who derived the symmetric rank-one updating formula, and his name was also attributed to Broyden's methods and Broyden family of quasi-Newton methods. After leaving the University of Essex, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Linear Algebra
Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices to develop computer algorithms that minimize the error introduced by the computer, and is also concerned with ensuring that the algorithm is as efficient as possible. Numerical linear algebra aims to solve problems of continuous mathematics using finite precision computers, so its applications to the natural and social scienc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Electric Company
The English Electric Company Limited (EE) was a British industrial manufacturer formed after World War I by amalgamating five businesses which, during the war, made munitions, armaments and aeroplanes. It initially specialised in industrial electric motors and transformers, locomotives and traction equipment, diesel motors and steam turbines. Its products were later expanded to include consumer electronics, nuclear reactors, guided missiles, military aircraft and mainframe computers. Two English Electric aircraft designs became landmarks in British aeronautical engineering; the Canberra and the Lightning. In 1960, English Electric Aircraft (40%) merged with Vickers (40%) and Bristol (20%) to form British Aircraft Corporation. In 1968 English Electric's operations were merged with GEC's, the combined business employing more than 250,000 people. Foundation Aiming to turn their employees and other assets to peaceful productive purposes, the owners of a series of businesses dec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aberystwyth University
Aberystwyth University () is a Public university, public Research university, research university in Aberystwyth, Wales. Aberystwyth was a founding member institution of the former federal University of Wales. The university has over 8,000 students studying across three academic faculties and 17 departments. Founded in 1872 as University College Wales, Aberystwyth, it became a founder member of the University of Wales in 1894, and changed its name to the University College of Wales, Aberystwyth. In the mid-1990s, the university again changed its name to become the University of Wales, Aberystwyth. On 1 September 2007, the University of Wales ceased to be a federal university and Aberystwyth University became independent again. The annual income of the institution for 2022–2023 was £130.8 million of which £22.2 million was from research grants and contracts, with an expenditure of £127.8 million. History In the middle of the 19th century, eminent Welsh p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Essex
The University of Essex is a public university, public research university in Essex, England. Established by royal charter in 1965, it is one of the original plate glass university, plate glass universities. The university comprises three campuses in the county, in Southend-on-Sea and Loughton with its primary campus in Wivenhoe Park, Colchester. Essex has a largely diverse student community and holds partnerships with more than 100 global higher education institutions. It was named Times Higher Education University of the Year, University of the Year at the Times Higher Education awards, ''Times Higher Education'' Awards in 2018. Essex's Department of Government received Regius Professorship conferred by Queen Elizabeth II in 2013 and the university was awarded the Queen's Anniversary Prize on two occasions for advancing human rights in 2009 and social and economic research in 2017. In the 2025 rankings of British universities, Essex is ranked 30th in the Complete University ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Bologna
The University of Bologna (, abbreviated Unibo) is a Public university, public research university in Bologna, Italy. Teaching began around 1088, with the university becoming organised as guilds of students () by the late 12th century. It is the List of oldest universities in continuous operation, oldest university in continuous operation in the world, and the first degree-awarding institution of higher learning.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hilde''A History of the University in Europe: Volume 1, Universities in the Middle Ages'' Cambridge University Press, 1992, , pp. 47–55 The university's emblem carries the motto, ''Alma Mater Studiorum'' ("Nourishing mother of studies"), and the date ''A.D. 1088''. With over 90,000 students, the University of Bologna is one of the List of largest universities by enrollment, largest universities in Europe. The university saw the first woman to earn a university degree ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Broyden's Method
In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in variables. It was originally described by C. G. Broyden in 1965. Newton's method for solving uses the Jacobian matrix, , at every iteration. However, computing this Jacobian can be a difficult and expensive operation; for large problems such as those involving solving the Kohn–Sham equations in quantum mechanics the number of variables can be in the hundreds of thousands. The idea behind Broyden's method is to compute the whole Jacobian at most only at the first iteration, and to do rank-one updates at other iterations. In 1979 Gay proved that when Broyden's method is applied to a linear system of size , it terminates in steps, although like all quasi-Newton methods, it may not converge for nonlinear systems. Description of the method Solving single-variable nonlinear equation In the secant method, we replace the first derivative at with the finite-difference approximation: : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ABS Methods
ABS usually refers to: * Acrylonitrile butadiene styrene, a common plastics polymer * Anti-lock braking system, in vehicles Abs usually refers to: * Rectus abdominis muscle ("abdominal muscle" or "abs") of humans and some mammals * Abdominal muscles (colloquial) ABS or Abs may also refer to: Arts and media Broadcasting * ABS (TV station), Australian Broadcasting Corporation's television station in Adelaide, Australia * ABS network (Arab Broadcasting Services) * Akita Broadcasting System, Japan * Amalgamated Broadcasting System, former US radio network * ABS-CBN Corporation, a Philippine media and entertainment conglomerate * ABS-CBN Corporation#History, Alto Broadcasting System, a Philippines company later ABS-CBN * ABS-CBN, a Philippine television network * Antigua Broadcasting Service, state broadcaster of Antigua and Barbuda Music * A.B.'s, a Japanese 1980s instrumental band * American Bach Soloists, chamber music ensemble * Abz Love, British singer Other media * Abs Denh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century British Mathematicians
File:1st century collage.png, From top left, clockwise: Jesus is crucified by Roman authorities in Judaea (17th century painting). Four different men (Galba, Otho, Vitellius, and Vespasian) claim the title of Emperor within the span of a year; The Great Fire of Rome (18th-century painting) sees the destruction of two-thirds of the city, precipitating the empire's first persecution against Christians, who are blamed for the disaster; The Roman Colosseum is built and holds its inaugural games; Roman forces besiege Jerusalem during the First Jewish–Roman War (19th-century painting); The Trưng sisters lead a rebellion against the Chinese Han dynasty (anachronistic depiction); Boudica, queen of the British Iceni leads a rebellion against Rome (19th-century statue); Knife-shaped coin of the Xin dynasty., 335px rect 30 30 737 1077 Crucifixion of Jesus rect 767 30 1815 1077 Year of the Four Emperors rect 1846 30 3223 1077 Great Fire of Rome rect 30 1108 1106 2155 Boudican revolt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
