John G.F. Francis (born 1934) is an English computer scientist, who in 1961 published the

QR algorithm In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix. The QR algorithm was developed in the late 1950s by John G. F. Francis and by ...

for computing the

eigenvalues and eigenvectors In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denote ...

of matrices, which has been named as one of the ten most important

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s of the twentieth century. The algorithm was also proposed independently by Vera N. Kublanovskaya of the

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

in the same year. Francis was born in

London London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...

in 1934. In 1954 he worked for the

National Research Development Corporation The National Research Development Corporation (NRDC) was a non-departmental government body established by the British Government to transfer technology from the public sector to the private sector. History The NRDC was established by Attlee's Lab ...

(NRDC). In 1955–1956 he attended

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209 and granted a royal charter by Henry III of England, Henry III in 1231, Cambridge is the world' ...

, but did not complete a degree. He then returned to the NRDC, where he served as assistant to

Christopher Strachey Christopher S. Strachey (; 16 November 1916 – 18 May 1975) was a British computer scientist. He was one of the founders of denotational semantics, and a pioneer in programming language design and computer time-sharing.F. J. Corbató, et al. ...

. At this time he devised the QR transformation. In 1961 he left the NRDC to work at Ferranti Corporation, Ltd. and then at the

University of Sussex , mottoeng = Be Still and Know , established = , type = Public research university , endowment = £14.4 million (2020) , budget = £319.6 million (2019–20) , chancellor = Sanjeev Bhaskar , vice_chancellor = Sasha Roseneil , ...

. Subsequently, he had positions with various industrial organizations and consultancies. His interests encompassed

artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech r ...

computer languages A computer language is a formal language used to communicate with a computer. Types of computer languages include: * Construction language – all forms of communication by which a human can specify an executable problem solution to a comput ...

, and systems engineering, although he never returned to the field of

numerical computation Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...

. Gene Golub (2007)
John Francis, Co-Inventor of QR
NA-Net mailing list, 19 August 2007. By 1962, Francis had left the field of

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods ...

, and subsequently had no idea of the impact his work on the QR algorithm had had, until re-contacted by Gene Golub and Frank Uhlig in 2007, by which time he was retired and living in

Hove Hove is a seaside resort and one of the two main parts of the city of Brighton and Hove, along with Brighton in East Sussex, England. Originally a "small but ancient fishing village" surrounded by open farmland, it grew rapidly in the 19th c ...

, England (near Brighton). Still in good health, he was the opening speaker at a mini-symposium that marked 50 years of the QR algorithm, held at th
23rd Biennial Conference on Numerical Analysis
in Glasgow in June 2009. Francis was awarded a University of Sussex honorary doctorate in July 2015.

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Further reading