Charles George Broyden (3 February 1933 – 20 May 2011) was a mathematician who specialized in
optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
problems and
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. ...
.
While a physicist working at
English Electric Company
N.º UIC: 9094 110 1449-3 (Takargo Rail)
The English Electric Company Limited (EE) was a British industrial manufacturer formed after the Armistice of 11 November 1918, armistice of World War I by amalgamating five businesses which, during th ...
from 1961–1965, he adapted the
Davidon–Fletcher–Powell formula The Davidon–Fletcher–Powell formula (or DFP; named after William C. Davidon, Roger Fletcher (mathematician), Roger Fletcher, and Michael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfie ...
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 1965–1967.
He later became a senior lecturer at
University of Essex
The University of Essex is a public university, public research university in Essex, England. Established by royal charter in 1965, Essex is one of the original plate glass university, plate glass universities. Essex's shield consists of the an ...
from 1967–1970,
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, he continued his research career in the Netherlands and Italy, being awarded the chair at
University of Bologna
The University of Bologna ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the oldest university in continuo ...
. In later years, he began focusing on numerical linear algebra, in particular conjugate gradient methods and their taxonomy.
Broyden died from complications of a severe stroke at the age of 78. He was survived by his wife, Joan, and their three children Chris, Jane and Nick.
A Charles Broyden Prize was established in 2009 to "honor this remarkable researcher" by Optimization Methods and Software in the international optimization community.
See also
*
Broyden's method
In numerical analysis, Broyden's method is a quasi-Newton method Quasi-Newton methods are methods used to either find zeroes or local maxima and minima of functions, as an alternative to Newton's method. They can be used if the Jacobian or Hessian ...
*
BFGS method
*
ABS methods ABS methods, where the acronym contains the initials of Jozsef Abaffy, Charles G. Broyden and Emilio Spedicato, have been developed since 1981 to generate a large class of algorithms for the following applications:
* solution of general linear alge ...
References
{{DEFAULTSORT:Broyden, Charles George
20th-century British mathematicians
21st-century British mathematicians
People educated at Newport Free Grammar School
1933 births
2011 deaths