Charles George Broyden
Mathematician
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Why Is Charles George Broyden Influential?
(Suggest an Edit or Addition)According to Wikipedia, Charles George Broyden was a mathematician who specialized in optimization problems and numerical linear algebra. While a physicist working at English Electric Company from 1961–1965, 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 1965–1967. He later became a senior lecturer at University of Essex from 1967–1970, where he independently discovered the Broyden–Fletcher–Goldfarb–Shanno 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. In later years, he began focusing on numerical linear algebra, in particular conjugate gradient methods and their taxonomy.
Charles George Broyden's Published Works
Published Works
- A Class of Methods for Solving Nonlinear Simultaneous Equations (1965) (2346)
- The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations (1970) (2246)
- The Convergence of a Class of Double-rank Minimization Algorithms 2. The New Algorithm (1970) (1518)
- Quasi-Newton methods and their application to function minimisation (1967) (604)
- On the Local and Superlinear Convergence of Quasi-Newton Methods (1973) (469)
- A New Method of Solving Nonlinear Simultaneous Equations (1969) (149)
- The convergence of single-rank quasi-Newton methods (1970) (108)
- The convergence of an algorithm for solving sparse nonlinear systems (1971) (106)
- On the discovery of the “good Broyden” method (2000) (46)
- Krylov solvers for linear algebraic systems (2004) (43)
- Large Sparse Sets of Linear Equations (1972) (34)
- A simple algebraic proof of Farkas's lemma and related theorems (1998) (33)
- Penalty functions, Newton's method, and quadratic programming (1988) (30)
- A smooth sequential penalty function method for solving nonlinear programming problems (1984) (29)
- On theorems of the alternative (2001) (25)
- Implementation of different computational variations of biconjugate residual methods (2001) (22)
- On the numerical stability of Huang's and related methods (1985) (20)
- A new taxonomy of conjugate gradient methods (1996) (13)
- A breakdown of the block CG method (1996) (11)
- QUASI-NEWTON, OR MODIFICATION METHODS**This work has done while the author was Visiting Research Professor, Department of Computer Science, Cornell University, and was supported by NSF Grant #GJ-27528. (1973) (11)
- Some generalisations of the theory of successive over-relaxation (1964) (10)
- Block conjugate gradient methods (1993) (10)
- Basic Matrices: An Introduction to Matrix Theory and Practice (1975) (8)
- Krylov Solvers for Linear Algebraic Systems: Krylov Solvers (2004) (8)
- On the numerical stability of Huang's update (1989) (8)
- On convergence criteria for the method of successive over-relaxation (1964) (8)
- Error Propagation in Numerical Processes (1974) (7)
- A Comparison of Three Basic Conjugate Direction Methods (1996) (7)
- Some aspects of consistent ordering (1968) (7)
- A Mark-Scaling Algorithm (1983) (5)
- A NEW Method of Polynomial Deflation (1975) (5)
- Resource allocation problems: Algorithmic approaches: T. IBARAKI and N. KATOH MIT Press, Cambridge, MA, 1988. $50.50, xiii + 229 pages (1989) (3)
- Some LP algorithms using orthogonal matrices (1995) (2)
- A note on the block conjugate gradient method of O'leary (1995) (2)
- An Alternative Derivation of the Simplex Method (1966) (2)
- On degeneracy in linear complementarity problems (1991) (2)
- Lemke's method—a recursive approach (1990) (2)
- Introduction — the Tools of the Trade (1975) (2)
- Linear Equations in Optimisation (1994) (1)
- Certification of Algorithm 66: INVRS (1962) (1)
- Classical Methods for Linear Equations (1991) (1)
- Duality in conjugate gradient methods (1999) (1)
- An algorithm for the solution of certain kinds of linear equations (1966) (0)
- The Practical Solution of Linear Equations (1975) (0)
- A Matrix Problem (C. G. Broyden) (1983) (0)
- The CG methods - a brief review (2000) (0)
- On the convergence of Krylov linear equation solvers (2001) (0)
- Further Properties of Linear Equations (1975) (0)
- Scalar Functions of a Vector (1975) (0)
- Some Elementary Consequences of Linear Independence (1975) (0)
- A Note on Guinand's Theorem (1978) (0)
- Matrix and Vector Norms (1975) (0)
- The Practical Evaluation of Eigenvalues and Eigenvectors (1975) (0)
- A Matrix Problem (1982) (0)
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