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Simpson Rule
In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761). The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads \int_a^b f(x) \, dx \approx \frac \left (a) + 4f\left(\frac\right) + f(b)\right In German and some other languages, it is named after Johannes Kepler, who derived it in 1615 after seeing it used for wine barrels (barrel rule, ). The approximate equality in the rule becomes exact if is a polynomial up to and including 3rd degree. If the 1/3 rule is applied to ''n'' equal subdivisions of the integration range 'a'', ''b'' one obtains the composite Simpson's 1/3 rule. Points inside the integration range are given alternating weights 4/3 and 2/3. Simpson's 3/8 rule, also called Simpson's second rule, requires one more function evaluation inside the integration range and gives lower error bounds, but does not improve the order of the error. If the 3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Simpson (name)
Simpson is an English/Scottish patronymic surname from the medieval masculine given name 'Simme', a medieval variant of 'Simon (surname), Simon'. The earliest public record of the name was in 1353 in Staffordshire, West Midlands (region), West Midlands region of England. Notable surnames A *Aaron Simpson (other), several people *Adam Simpson (born 1976), Australian rules footballer *Adele Simpson (1903–1995), American child performer and fashion designer *Adrian Simpson (born 1971), British TV presenter *Adrienne Simpson (1943–2010), New Zealand broadcaster, historian, musicologist and writer *Al Simpson (1916–1976), American football coach *Alan Simpson (other), several people *Albert Benjamin Simpson (1843–1919), Canadian evangelist *Alex Simpson (1924–2008), Scottish soccer player *Alexander Simpson (other), several people *A. W. B. Simpson (Alfred, 1931–2011), British legal historian *Alfred Allen Simpson (1875–1939), South Austra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |