X-Nico

4 unusual facts about Horner's method


Horner's method

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.

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.

Paul de Casteljau

Other methods, such as Horner's method and forward differencing, are faster for calculating single points but are less robust.

William George Horner

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.


Baillie–PSW primality test

# 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.

Bairstow's method

The algorithm first appeared in the appendix of the 1920 book "Applied Aerodynamics" by Leonard Bairstow.

BC-STV

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

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.

Chuck Horner

During the Desert Shield phase of the conflict, Horner briefly served as Commander-in-Chief — Forward of U.S. Central Command; while General Schwarzkopf was still in the United States.

Dodgson's method

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.

Ed Ochester

Since 1972 he and his wife Britt Horner have lived on a small farm in Armstrong County, Pennsylvania.

Find first set

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.

François Budan de Boislaurent

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.

Generalized estimating equation

The parameter estimates solve U(β)=0 and are typically obtained via the Newton-Raphson algorithm.

Halley's method

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).

Harry Horner

Following Max Reinhardt to New York, Harry Horner assisted Reinhardt in his staging of the Biblical musical spectacle "The Eternal Road" ("Der Weg der Verheissung"); the production had music by Kurt Weill; conducted by Harry Horner; opening at the Manhattan Opera House 1/7/1937-5/15/1937 with scenic design, costume design and lighting by Norman Bel Geddes.

Heinrich Wilhelm Gottfried von Waldeyer-Hartz

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.

Henry Horner Homes

Henry Horner is bordered between Damen Avenue and Lake Street near the United Center.

Hermann Gummel

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.

Horner's syndrome

In France and Italy, Claude Bernard is also eponymized with the condition ("Claude Bernard-Horner syndrome").

Implied volatility

When forced to solve for vega numerically, it usually turns out that Brent's method is more efficient as a root-finding technique.

While there are many techniques for finding roots, two of the most commonly used are Newton's method and Brent's method.

Johan Frederik Steffensen

Steffensen's inequality and Steffensen's method (an iterative numerical method) are named after him.

John Horner

John Horner, a fictional character in The Adventure of the Blue Carbuncle, a Sherlock Holmes story by Sir Arthur Conan Doyle

Karl Heun

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.

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.

LETTERS

In addition to the Author and Germaine Pitt (or 'Lady Amherst', unrelated to any of Barth's previous novels), the correspondents are: Todd Andrews (from The Floating Opera), Jacob Horner (from The End of the Road), A.B. Cook (a descendent of Burlingame in The Sot-Weed Factor), Jerome Bray (associated with Giles Goat-Boy and Chimera) and Ambrose Mensch (from Lost in the Funhouse).

Little Jack Horner

During the journey Horner opened the pie and extracted the deeds of the manor of Mells in Somerset, which he kept for himself.

London Colosseum

Initial plans to sell panoramic views came to nothing, but an elaborate scheme to create a 360-degree panorama on the inside of a dome of the Colosseum, specially built in Regents Park (and resembling the Roman Pantheon rather than the Roman Colosseum), came to fruition, but at such expense that its principal backer, Rowland Stephenson MP, had to flee to America in 1828, soon followed by Horner.

Louis Weisner

Louis Weisner (born 1899) was a Canadian mathematician at the University of New Brunswick who introduced Weisner's method.

Macaulay's method

The first English language description of the method was by Macaulay.

Memphis Cathouse Blues

Her exclusive client is Sheriff T.J. Thomson (Mike Horner), but he can't help her against Reverand Pritchit (R.J. Reynolds) who sends Deacon Davis (Herschel Savage) and Brother Pyle (Jon Martin) to demonstrate outside.

Michael Eytzinger

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.

Michael Hagemeister

P.A. Florenskiĭ i kulʹtura ego vremeni: P.A. Florenskij e la cultura della sua epoca: atti del convegno internazionale, Università degli Studi di Bergamo, 10-14 gennaio 1988 / a cura di Michael Hagemeister e Nina Kauchtschischwili (Marburg: Blaue Hörner, 1995)

Moss Icon

In 1990 a splinter project of Moss Icon was formed called Breathing Walker, containing all four members of Moss Icon plus Alex Badertscher on bass, Zak Fusciello on percussion, and Tim Horner on violin.

Newton's method

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.

Newton's method was first published in 1685 in A Treatise of Algebra both Historical and Practical by John Wallis.

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).

Nicholas Horner

Nicholas Horner (born at Grantley, Yorkshire, England, date of birth unknown; executed at Smithfield, 4 March 1590) was an English Roman Catholic

Orbitalis muscle

Horner's syndrome causes paralysis of the structures of the eye and orbit that receive sympathetic innervation.

Phil Horner

Horner began his career with Leicester City in 1983, but he only made ten league appearances in five years at Filbert Street and spent a short spell on loan at Rotherham United in the 1985–86 season.

Powell

Powell's method, algorithm for finding the minimum of a non-differentiable function

Proportional hazards model

Using this score function and Hessian matrix, the partial likelihood can be maximized using the Newton-Raphson algorithm.

Quadratic function

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.

Sam Horner

Samuel Watson Horner, III (born March 4, 1938 in Fort Sill, Oklahoma) is a former American football halfback, defensive back, and punter in the National Football League for the Washington Redskins and the New York Giants.

Seki Takakazu

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.

The Truth About Mother Goose

Little Jack Horner: Thomas Horner (steward to Richard Whiting, the last abbot of Glastonbury), allegedly stealing a title deed in transit to Henry VIII of England.

Ward's method

Jain, A. K. and Dubes, R. C. (1988), Algorithms for Clustering Data, New Jersey: Prentice–Hall.

William Monson, 1st Viscount Monson

third, Elizabeth (died 1695), second daughter of Sir George Reresby, of Thrybergh, Yorkshire, widow of Sir Francis Foljambe, 1st Baronet, of Aldwark in the same county, and of Edward, younger son of Sir John Horner of Mells, Somerset.


see also