The algorithm first appeared in the appendix of the 1920 book "Applied Aerodynamics" by Leonard Bairstow.
Born in 1880 in Halifax, Bairstow is best remembered for his work in aviation and for Bairstow's method for arbitrarily finding the roots of polynomials.
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Bairstow's father, David, was a former Test cricketer for England, and it was a surprise when the Peakites, without the relative experience of Karl Krikken and defensive technique of Steve Griffiths, called upon the young Bairstow as their cover man.
# If n is a perfect square, then step 3 will never yield a D with (D/n) = −1; this is not a problem because perfect squares are easy to detect using Newton's method for square roots.
If votes are transferred because a candidate has exceeded the quota required to win, all of that candidate's ballots are examined for transfer votes (Senatorial rules), unlike the method used for the Irish Dáil in which, after a candidate has reached the quota, only the last parcel of votes transferred to that candidate are examined for further preferences (the Hare method).
Carlo Alberto Castigliano (9 November 1847, Asti – 25 October 1884, Milan) was an Italian mathematician and physicist known for Castigliano's method for determining displacements in a linear-elastic system based on the partial derivatives of strain energy.
In short, we must find the voting profile with minimum Kendall tau distance from the input, such that it has a Condorcet winner; they are declared the victor.
The expression 16 − clz(x − 1)/2 is an effective initial guess for computing the square root of a 32-bit integer using Newton's method.
Budan's work on approximation was studied by Horner in preparing his celebrated article in the Philosophical Transactions of the Royal Society of London in 1819 that gave rise to the term Horner's method; Horner comments there and elsewhere on Budan's results, at first being sceptical of the value of Budan's work, but later warming to it.
The parameter estimates solve U(β)=0 and are typically obtained via the Newton-Raphson algorithm.
Halley's method can be viewed as exactly finding the roots of a linear-over-linear Padé approximation to the function, in contrast to Newton's method/Secant method (approximates/interpolates the function linearly) or Cauchy's method/Muller's method (approximates/interpolates the function quadratically).
Waldeyer used the path-breaking discoveries by neuroanatomists (and later Nobel Prize winners) Camillo Golgi (1843–1926) and Santiago Ramón y Cajal (1852–1934), who had used the silver nitrate method of staining nerve tissue (Golgi's method) to formulate a short brilliant synthesis, even though he did not contribute with any original observations.
Among the most important of his contributions are the Gummel–Poon model which made accurate simulation of bipolar transisors possible and which was central to the development of the SPICE program; Gummel's method, used to solve the equations for the detailed behavior of individual bipolar transistors,; and the Gummel plot, used to characterize bipolar transistors.
Ulrich Libbrecht (at the time teaching in school, but subsequently a professor of comparative philosophy) gave a detailed description in his doctoral thesis of Qin's method, he concluded: It is obvious that this procedure is a Chinese invention....the method was not known in India.
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As it also happened, Henry Atkinson, of Newcastle, devised a similar approximation scheme in 1809; he had consulted his fellow Geordie, Charles Hutton, another specialist and a senior colleague of Barlow at the Royal Military Academy, Woolwich, only to be advised that, while his work was publishable, it was unlikely to have much impact.
When forced to solve for vega numerically, it usually turns out that Brent's method is more efficient as a root-finding technique.
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While there are many techniques for finding roots, two of the most commonly used are Newton's method and Brent's method.
Steffensen's inequality and Steffensen's method (an iterative numerical method) are named after him.
Karl Heun (born 3 April 1859, Wiesbaden; died 10 January 1929, Karlsruhe) was a German mathematician who introduced Heun's equation, Heun functions, and Heun's method.
He held the Zaharoff Chair of Aviation at Imperial College London from 1920-1949 and became Professor Sir Leonard Bairstow.
Louis Weisner (born 1899) was a Canadian mathematician at the University of New Brunswick who introduced Weisner's method.
The first English language description of the method was by Macaulay.
Eytzinger’s method was used by Jerónimo de Sosa, in his work Noticia de la gran casa de los marqueses de Villafranca in 1676, and was popularized by Stephan Kekulé von Stradonitz in his Ahnentafel-atlas in 1898.
The basic idea of Nash's solution of the embedding problem is the use of Newton's method to prove the existence of a solution to the above system of PDEs.
In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
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Newton's method was first published in 1685 in A Treatise of Algebra both Historical and Practical by John Wallis.
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The name "Newton's method" is derived from Isaac Newton's description of a special case of the method in De analysi per aequationes numero terminorum infinitas (written in 1669, published in 1711 by William Jones) and in De metodis fluxionum et serierum infinitarum (written in 1671, translated and published as Method of Fluxions in 1736 by John Colson).
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In 1690, Joseph Raphson published a simplified description in Analysis aequationum universalis.
Other methods, such as Horner's method and forward differencing, are faster for calculating single points but are less robust.
Powell's method, algorithm for finding the minimum of a non-differentiable function
Using this score function and Hessian matrix, the partial likelihood can be maximized using the Newton-Raphson algorithm.
The solutions to this equation are called the roots of the quadratic polynomial, and may be found through factorization, completing the square, graphing, Newton's method, or through the use of the quadratic formula.
Chinese algebra discovered numerical evaluation (Horner's method, re-established by William George Horner in the 19th century) of arbitrary degree algebraic equation with real coefficients.
A replica of the Bairstow eagles is seen in a World War I monument in Middletown, Delaware.
Jain, A. K. and Dubes, R. C. (1988), Algorithms for Clustering Data, New Jersey: Prentice–Hall.
His contribution to approximation theory is honoured in the designation Horner's method, in particular respect of a paper in Philosophical Transactions of the Royal Society of London for 1819.