Charles William Clenshaw (15 March 15, 1926, Southend-on-Sea, Essex – 23 September 2004) was an English mathematician, specializing in numerical analysis. He is known for the Clenshaw algorithm (1955) and Clenshaw–Curtis quadrature (1960). In a 1984 paper Beyond Floating Point, Clenshaw and Frank W. J. Olver introduced symmetric level-index arithmetic.
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. 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, Teddington. 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. 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.
Charles was head of Lancaster’s mathematics department from 1975 to 1978 and from 1982 to 1984, but in the 1980s, the government instituted broad cuts in the number of faculty members in many universities. As department head, Charles was instructed to select one member for dismissal. Regarding this instruction as totally unfair, he dismissed himself — taking early retirement in 1985. He was then honoured as professor emeritus.
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.