Charles William Clenshaw (15 March 1926,

Southend-on-Sea Southend-on-Sea (), commonly referred to as Southend (), is a coastal city and unitary authority area with borough status in southeastern Essex, England. It lies on the north side of the Thames Estuary, east of central London. It is bordered ...

Essex Essex () is a county in the East of England. One of the home counties, it borders Suffolk and Cambridgeshire to the north, the North Sea to the east, Hertfordshire to the west, Kent across the estuary of the River Thames to the south, and G ...

– 23 September 2004) was an English mathematician, specializing in numerical analysis. He is known for the

Clenshaw algorithm In numerical analysis, the Clenshaw algorithm, also called Clenshaw summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials. Note that this paper is written in terms of the ''Shifted'' Chebyshev polynomials of the ...

(1955) and

Clenshaw–Curtis quadrature Clenshaw–Curtis quadrature and Fejér quadrature are methods for numerical integration, or "quadrature", that are based on an expansion of the integrand in terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = \cos ...

(1960). In a 1984 paper ''Beyond Floating Point'', Clenshaw and Frank W. J. Olver introduced

symmetric level-index arithmetic The level-index (LI) representation of numbers, and its algorithms for arithmetic operations, were introduced by Charles Clenshaw and Frank Olver in 1984. The symmetric form of the LI system and its arithmetic operations were presented by Clensha ...

Biography

Charles William Clenshaw attended the local high school in Southend-on-Sea from 1937 to 1943. In 1946 he graduated with a degree in mathematics and physics from

King's College London King's College London (informally King's or KCL) is a public research university located in London, England. King's was established by royal charter in 1829 under the patronage of King George IV and the Duke of Wellington. In 1836, King's ...

. There in 1948 he graduated with a PhD in mathematics. From 1945 to 1969 he was a mathematician at the UK's National Physical Laboratory (NPL) in

Bushy Park Bushy Park in the London Borough of Richmond upon Thames is the second largest of London's Royal Parks, at in area, after Richmond Park. The park, most of which is open to the public, is immediately north of Hampton Court Palace and Hampton ...

Teddington Teddington is a suburb in south-west London in the London Borough of Richmond upon Thames. In 2021, Teddington was named as the best place to live in London by ''The Sunday Times''. Historically in Middlesex, Teddington is situated on a long m ...

. There from 1961 to 1969 he was a senior principal scientific officer and headed the numerical methods group in NPL's mathematics division. In 1969 he resigned from NPL and accepted an appointment as professor of numerical analysis at

Lancaster University Lancaster University (legally The University of Lancaster) is a public university, public research university in Lancaster, Lancashire, Lancaster, Lancashire, England. The university was established in 1964 by royal charter, as one of several pla ...

. He and Emlyn Howard Lloyd (1918–2008), professor of statistics, strengthened the mathematics department, and the department's numerical analysis group became one of best in the UK. The mathematics department hosted the first four summer schools in numerical analysis sponsored by the UK's

Engineering and Physical Sciences Research Council The Engineering and Physical Sciences Research Council (EPSRC) is a British Research Council that provides government funding for grants to undertake research and postgraduate degrees in engineering and the physical sciences, mainly to universi ...

.EPSRC numerical analysis summer schools were held at various UK universities, including Lancaster, Leicester, and Durham. The ninth EPSRC summer school was held at Durham University in 2000. Clenshaw did research in approximation theory based on Chebyshev polynomials, software development supporting trigonometric functions, Bessel functions, etc., and computer arithmetic systems. His PhD students include William Allan Light (1950–2002). Upon his death, Clenshaw was survived by his wife, three sons, a daughter, and ten grandchildren. Sgt. Ian Charles Cooper Clenshaw (1918–1940), one of Charles William Clenshaw's brothers, was officially the first RAF pilot to be killed in the Battle of Britain.

Selected publications

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References

{{DEFAULTSORT:Clenshaw, Charles William 1926 births 2004 deaths Alumni of King's College London Academics of Lancaster University English computer scientists 20th-century English mathematicians 21st-century English mathematicians Approximation theorists Numerical analysts