computer science

John G. F. Francis

John G. F. Francis is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand John G. F. Francis rather than just read about it. In short: John G.F. Francis (born 1934) is an English computer scientist, who in 1961 published the QR algorithm for computing the eigenvalues and eigenvectors of matrices, which has been named as one of the ten most important algorithms of the twentieth century.

Key takeaways

John G. F. Francis belongs to computer science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect John G. F. Francis to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of John G. F. Francis from memory before moving on to harder problems.

Reference excerpt

John G.F. Francis (born 1934) is an English computer scientist, who in 1961 published the QR algorithm for computing the eigenvalues and eigenvectors of matrices, which has been named as one of the ten most important algorithms of the twentieth century. The algorithm was also proposed independently by Vera N. Kublanovskaya of the Soviet Union in the same year. Francis was born in London in 1934. In 1954 he worked for the National Research Development Corporation (NRDC). In 1955–1956 he attended Cambridge University, but did not complete a degree. He then returned to the NRDC, where he served as assistant to Christopher Strachey. 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. Subsequently, he had positions with various industrial organizations and consultancies. His interests encompassed artificial intelligence, computer languages, and systems engineering, although he never returned to the field of numerical computation. By 1962, Francis had left the field of numerical analysis, 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, 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 the 23rd Biennial Conference on Numerical Analysis in Glasgow in June 2009. Francis was awarded a University of Sussex honorary doctorate in July 2015.

References

Further reading Gene Golub, Frank Uhlig (2009), "The QR algorithm: 50 years later – its genesis by John Francis and Vera Kublanovskaya, and subsequent developments", IMA Journal of Numerical Analysis, vol. 29, no. 3, pages 467-485.advanced publication online[link removed] doi:10.1093/imanum/drp012

Worked examples

Example 1 — a first encounter with John G. F. Francis

Start with the simplest possible case. Write down what John G. F. Francis claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to John G. F. Francis before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about John G. F. Francis ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of John G. F. Francis

In research: John G. F. Francis appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses John G. F. Francis in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: John G. F. Francis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1934 births, English computer scientists, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for John G. F. Francis outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study John G. F. Francis in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what John G. F. Francis means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain John G. F. Francis out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is John G. F. Francis in simple terms?

Why does John G. F. Francis matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study John G. F. Francis?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on John G. F. Francis.