Leslie Fox
Encyclopedia
Leslie Fox was a British
mathematician
noted for his contribution to numerical analysis
.
Fox studied mathematics as a scholar of Christ Church, Oxford
graduating with a First in 1939 and continued to undertake research in the engineering department. While working on his D.Phil.
in computational and engineering mathematics under the supervision of Sir Richard Southwell he was also engaged in highly secret war work. He worked on the numerical solution of partial differential equation
s at a time when numerical linear algebra was performed on a desk calculator. Computational efficiency and accuracy was thus even more important than in the days of electronic computers. Some of this work was published after the end of the Second World War jointly with his supervisor Richard Southwell
.
On gaining his doctorate in 1942 Fox joined the Admiralty Computing service. Following the war, in 1945 he went to work in the mathematics division of the National Physical Laboratory. He left the National Physical Laboratory in 1956 and spent a year at the University of California
. In 1957 Fox took up an appointment at Oxford University where he set up the Computing Laboratory. In 1963 Fox was appointed as Professor of Numerical Analysis at Oxford and Fellow of Balliol College, Oxford
.
Fox's laboratory at Oxford was one of the founding organisations of the Numerical Algorithms Group
, and Fox was also a dedicated supporter of the Institute of Mathematics and its Applications
(IMA). The Leslie Fox Prize for Numerical Analysis
of the IMA is named in his honour.
and is summarised here. His early work with Southwell was concerned with the numerical solution of partial differential equations arising in engineering problems that, due to the complexity of their geometry, did not have analytical solutions. Southwell's group developed efficient and accurate relaxation method
s, which could be implemented on desk calculators. Fox's contributions were particularly notable because he combined practical skills with theoretical advances in relaxation methods, which were to become important areas of research in numerical analysis. During the 1950 automatic electronic computers were replacing manual electro-mechanical devices. This led to different problems in the implementation of numerical algorithms, however the approach of approximating a partial differential equation by finite difference method
and thus reducing the problem to a system of linear equations was the same. Careful analysis of the errors were a theme of many of Fox's early papers. His work at the Admiralty Computing Service and the National Physical Laboratory led to an interest in the computation of special functions, and his calculations were used in published tables. The techniques applied to the computation of special functions had much wider applicability including interpolation
, stability of recurrence relation
s and asymptotic behaviour.
During the 1950s the group at the National Physics Laboratory worked on numerical linear algebra
, and led to the publication of algorithms by Wilkinson
and others. While not directly involved in development of numerical software he supported others in this endeavour. Fox worked on procedures for solving differential equations in which accuracy of the solution is estimated using asymptotic estimates. Fox's paper on this in 1947 led to the work of Victor Pereyra error-correcting algorithms for boundary-value problems and Stetter's results on defect correction and the resulting order of convergence.
Fox was also interested in the treatment of singularities in partial differential equations, the Stefan problem
and other cases of free and moving boundaries. Many of these problems arose from his collaboration with mathematicians in industry through the Oxford Study Groups.
. He lectured widely on 'meaningless answers', describing some of the pitfalls of numerical computation from the uncritical use of simple methods
Fox played a signifficant part in the early days of the Numerical Algorithms Group
(NAG), which set out as a collaborative venture between Oxford, Nottingham
and Manchester
to provide a reliable and well-tested mathematical subroutine library. The Oxford Computing Laboratory was one of the founder members of NAG when it started in 1970, and Fox supported it strongly and he became a member of its council when the Group was incorporated in 1976 continuing in this capacity until 1984.
Fox was an active member of the Institute of Mathematics and its Applications from its beginnings, as a member of the Council and as an editor first of the main IMA Journal and later the specialised Journal of Numerical Analysis, started in 1981. The IMA marked his retirement from Oxford in 1983 by a special IMA symposium on 'The contributions of Leslie Fox to numerical analysis'.
His interests extended to mathematics in schools and he participated the development of the School Mathematics Project
, and was active in the local branch of the Mathematical Association
, of which he was President in 1964. The first winner of the IMA's Leslie Fox prize for Numerical Analysis
in 1985, Lloyd Nicholas Trefethen
, went on to be appointed to the chair in Numerical Analysis at Oxford that was created for Leslie Fox in 1963.
He was a keen sportsman and played football for the university Football Club as well as for Oxford City Football Club. At the National Physical Laboratory he was club tennis
champion and captain of the cricket team, he also distinguished himself as a sprinter in the civil service championships.
Fox, who had enjoyed good health up to 1981, suffered from heart problems during his retirement and died from a ruptured aneurysm in the John Radcliffe Hospital
, Oxford in 1992.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
noted for his contribution to numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
.
Fox studied mathematics as a scholar of Christ Church, Oxford
Christ Church, Oxford
Christ Church or house of Christ, and thus sometimes known as The House), is one of the largest constituent colleges of the University of Oxford in England...
graduating with a First in 1939 and continued to undertake research in the engineering department. While working on his D.Phil.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in computational and engineering mathematics under the supervision of Sir Richard Southwell he was also engaged in highly secret war work. He worked on the numerical solution of partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s at a time when numerical linear algebra was performed on a desk calculator. Computational efficiency and accuracy was thus even more important than in the days of electronic computers. Some of this work was published after the end of the Second World War jointly with his supervisor Richard Southwell
Richard V. Southwell
Sir Richard Vynne Southwell MA, LLD, FRS was a British mathematician who specialized in applied mechanics as an engineering science academic.- Education and career :...
.
On gaining his doctorate in 1942 Fox joined the Admiralty Computing service. Following the war, in 1945 he went to work in the mathematics division of the National Physical Laboratory. He left the National Physical Laboratory in 1956 and spent a year at the University of California
University of California
The University of California is a public university system in the U.S. state of California. Under the California Master Plan for Higher Education, the University of California is a part of the state's three-tier public higher education system, which also includes the California State University...
. In 1957 Fox took up an appointment at Oxford University where he set up the Computing Laboratory. In 1963 Fox was appointed as Professor of Numerical Analysis at Oxford and Fellow of Balliol College, Oxford
Balliol College, Oxford
Balliol College , founded in 1263, is one of the constituent colleges of the University of Oxford in England but founded by a family with strong Scottish connections....
.
Fox's laboratory at Oxford was one of the founding organisations of the Numerical Algorithms Group
Numerical Algorithms Group
The Numerical Algorithms Group is a software company which provides methods for the solution of mathematical and statistical problems, and offers services to users of HPC systems. Its products and services are employed by tens of thousands of users from Global 500 companies, universities,...
, and Fox was also a dedicated supporter of the Institute of Mathematics and its Applications
Institute of Mathematics and its Applications
The Institute of Mathematics and its Applications is the UK's chartered professional body for mathematicians and one of the UK's learned societies for mathematics ....
(IMA). The Leslie Fox Prize for Numerical Analysis
Leslie Fox Prize for Numerical Analysis
The Leslie Fox Prize for Numerical Analysis of the Institute of Mathematics and its Applications is a biennial prize established in 1985 by the IMA in honour of mathematician Leslie Fox . The prize honours "young numerical analysts worldwide" , and applicants submit papers for review...
of the IMA is named in his honour.
Mathematical work
A detailed description of Fox's mathematical research can be found in obituariesand is summarised here. His early work with Southwell was concerned with the numerical solution of partial differential equations arising in engineering problems that, due to the complexity of their geometry, did not have analytical solutions. Southwell's group developed efficient and accurate relaxation method
Relaxation method
In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems.Relaxation methods were developed for solving large sparse linear systems, which arose as finite-difference discretizations of differential equations...
s, which could be implemented on desk calculators. Fox's contributions were particularly notable because he combined practical skills with theoretical advances in relaxation methods, which were to become important areas of research in numerical analysis. During the 1950 automatic electronic computers were replacing manual electro-mechanical devices. This led to different problems in the implementation of numerical algorithms, however the approach of approximating a partial differential equation by finite difference method
Finite difference method
In mathematics, finite-difference methods are numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.- Derivation from Taylor's polynomial :...
and thus reducing the problem to a system of linear equations was the same. Careful analysis of the errors were a theme of many of Fox's early papers. His work at the Admiralty Computing Service and the National Physical Laboratory led to an interest in the computation of special functions, and his calculations were used in published tables. The techniques applied to the computation of special functions had much wider applicability including interpolation
Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
, stability of recurrence relation
Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms....
s and asymptotic behaviour.
During the 1950s the group at the National Physics Laboratory worked on numerical linear algebra
Numerical linear algebra
Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers. It is often a fundamental part of engineering and computational science problems, such as image and signal processing, Telecommunication, computational...
, and led to the publication of algorithms by Wilkinson
James H. Wilkinson
James Hardy Wilkinson was a prominent figure in the field of numerical analysis, a field at the boundary of applied mathematics and computer science particularly useful to physics and engineering.-Early life:...
and others. While not directly involved in development of numerical software he supported others in this endeavour. Fox worked on procedures for solving differential equations in which accuracy of the solution is estimated using asymptotic estimates. Fox's paper on this in 1947 led to the work of Victor Pereyra error-correcting algorithms for boundary-value problems and Stetter's results on defect correction and the resulting order of convergence.
Fox was also interested in the treatment of singularities in partial differential equations, the Stefan problem
Stefan problem
In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a partial differential equation , adapted to the case in which a phase boundary can move with time...
and other cases of free and moving boundaries. Many of these problems arose from his collaboration with mathematicians in industry through the Oxford Study Groups.
Fox's wider influence
While Fox influenced the development of numerical analysis through his undergraduate teaching and postgraduate supervision (he supervised around 19 doctoral students), industrial collaboration he also made significant contributions to course material for the Open UniversityOpen University
The Open University is a distance learning and research university founded by Royal Charter in the United Kingdom...
. He lectured widely on 'meaningless answers', describing some of the pitfalls of numerical computation from the uncritical use of simple methods
Fox played a signifficant part in the early days of the Numerical Algorithms Group
Numerical Algorithms Group
The Numerical Algorithms Group is a software company which provides methods for the solution of mathematical and statistical problems, and offers services to users of HPC systems. Its products and services are employed by tens of thousands of users from Global 500 companies, universities,...
(NAG), which set out as a collaborative venture between Oxford, Nottingham
University of Nottingham
The University of Nottingham is a public research university based in Nottingham, United Kingdom, with further campuses in Ningbo, China and Kuala Lumpur, Malaysia...
and Manchester
School of Mathematics, University of Manchester
The School of Mathematics at the University of Manchester is one of the largest mathematics departments in the United Kingdom, with around 80 academic staff and an undergraduate intake of roughly 400 a year and another 200 postgraduate students...
to provide a reliable and well-tested mathematical subroutine library. The Oxford Computing Laboratory was one of the founder members of NAG when it started in 1970, and Fox supported it strongly and he became a member of its council when the Group was incorporated in 1976 continuing in this capacity until 1984.
Fox was an active member of the Institute of Mathematics and its Applications from its beginnings, as a member of the Council and as an editor first of the main IMA Journal and later the specialised Journal of Numerical Analysis, started in 1981. The IMA marked his retirement from Oxford in 1983 by a special IMA symposium on 'The contributions of Leslie Fox to numerical analysis'.
His interests extended to mathematics in schools and he participated the development of the School Mathematics Project
School Mathematics Project
The School Mathematics Project is a developer of mathematics textbooks for secondary schools, based in Southampton in the UK.Now generally known as SMP, it began as a research project inspired by a 1961 conference chaired by Bryan Thwaites at the University of Southampton, which itself was...
, and was active in the local branch of the Mathematical Association
Mathematical Association
The Mathematical Association is a professional society concerned with mathematics education in the UK.-History:It was founded in 1871 as the Association for the Improvement of Geometrical Teaching and renamed to the Mathematical Association in 1897. It was the first teachers' subject organisation...
, of which he was President in 1964. The first winner of the IMA's Leslie Fox prize for Numerical Analysis
Leslie Fox Prize for Numerical Analysis
The Leslie Fox Prize for Numerical Analysis of the Institute of Mathematics and its Applications is a biennial prize established in 1985 by the IMA in honour of mathematician Leslie Fox . The prize honours "young numerical analysts worldwide" , and applicants submit papers for review...
in 1985, Lloyd Nicholas Trefethen
Lloyd Nicholas Trefethen
Lloyd Nicholas Trefethen FRS is professor of numerical analysis and head of the Numerical Analysis Group in the Mathematical Institute at the University of Oxford....
, went on to be appointed to the chair in Numerical Analysis at Oxford that was created for Leslie Fox in 1963.
Personal life
Leslie Fox's mother was Annie Vincent and his father was Job Senior Fox who was a coalminer. Leslie won a scholarship to Wheelwright Grammar School in Dewsbury which produced several notable scientists from the same period as Fox.He was a keen sportsman and played football for the university Football Club as well as for Oxford City Football Club. At the National Physical Laboratory he was club tennis
Tennis
Tennis is a sport usually played between two players or between two teams of two players each . Each player uses a racket that is strung to strike a hollow rubber ball covered with felt over a net into the opponent's court. Tennis is an Olympic sport and is played at all levels of society at all...
champion and captain of the cricket team, he also distinguished himself as a sprinter in the civil service championships.
Fox, who had enjoyed good health up to 1981, suffered from heart problems during his retirement and died from a ruptured aneurysm in the John Radcliffe Hospital
John Radcliffe Hospital
The John Radcliffe Hospital is a large tertiary teaching hospital in Oxford, England.It is the main teaching hospital for Oxford University and Oxford Brookes University. As such, it is a well-developed centre of medical research. It also incorporates the Medical School of the University of Oxford....
, Oxford in 1992.
Selected publications
- Leslie Fox, The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations, 1957, reprinted by Dover 1990 ISBN 0-486-66495-3
- L Fox, An introduction to numerical linear algebra, 1964, Oxford University Press, Oxford, England, ISBN 0-19-500325-X
- L Fox, D.F. Mayers, Numerical solution of ordinary differential equations. Chapman & Hall, London, 1987. ISBN 0-412-22650-2