X-Nico

unusual facts about Halley's method


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).


Aegospotami

This meteorite is believed to have been dislodged from a near-Earth orbit by the passing Halley's Comet.

Alexis Clairaut

He obtained an ingenious approximate solution of the problem of the three bodies; in 1750 he gained the prize of the St Petersburg Academy for his essay Théorie de la lune; the team made up of Clairaut, Jérome Lalande and Nicole Reine Lepaute successfully computed the date of the 1759 return of Halley's comet.

Arthur Storer

The comet became known as Storer's Comet, until Edmund Halley later predicted the comet's return; thereafter this celestial marvel was known as Halley's Comet.

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.

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.

Choke Canyon

Dr. David Lowell's (Collins) research is carried out in the canyon country of southern Utah and must be conducted at the same time Halley's Comet is passing over the earth.

Comet Hyakutake

It has been proposed that cometary collisions with Earth might have supplied a large proportion of the water in the oceans, but the high D/H ratio measured in Hyakutake and other comets such as Hale–Bopp and Halley's Comet have caused problems for this theory.

Crab Nebula

The exact time of the comet's return required the consideration of perturbations to its orbit caused by planets in the Solar System such as Jupiter, which Clairaut and his two colleagues Jérôme Lalande and Nicole-Reine Lepaute carried out more precisely than Halley, finding that the comet should appear in the constellation of Taurus.

Debre Berhan

Historian Richard Pankhurst offers the date of 1456 for the date of the founding of this church, providing a plausible argument that the light in the sky was Halley's Comet, which could have been in Shewa that year, although the traditional dates (10th day of the month of Maggabit, i.e. 6 or 7 March) do not coincide with the days that the comet was most visible (13 through 17 June).

Dengeki Sentai Changeman

He manages to approach Earth undetected by hiding himself into the tail of Halley's Comet, but is ultimately destroyed by the Changemen after they ride Change Robo deep onto his body and destroy its core.

Disjecta

Visual arts programming highlights include solo exhibitions by Anna Fidler, Chris Fraser, Peter Halley, Karl Burkheimer, Mark Licari, Avantika Bawa, Jenene Nagy, and Dan Gilsdorf.

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.

Halley's Comet Opal

It is so named because it was unearthed in 1986, a year when Halley's Comet could be seen from Earth.

Andamooka Opal, another named opal that is also known as the Queen's Opal

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.

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 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.

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.

Jesus: Kyōfu no Bio Monster

Halley's Comet has been approaching Mars for quite some time, and the nations of Earth send a mission to investigate the Comet, as some form of life has been detected inside the gas of the comet.

Johan Frederik Steffensen

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

Johann Carion

Andreas Perlach in a work on the comet of 1531 questioned whether his methods were purely astrological or involved magic.

John Zarnecki

In 1981, he moved to the University of Kent in Canterbury and became the project manager for the Dust Impact Detection System on board the Giotto probe that visited Halley's Comet.

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.

Liège Space Center

In the early 1980s, CSL participated in the development of the "Halley Multicolour Camera", which embarked aboard the spacecraft Giotto, photographed the nucleus of Halley's Comet in 1986.

Mike Gwilym

His most high-profile role was as Sid Halley in The Racing Game, a six-part Yorkshire Television series based on Dick Francis's 1965 novel Odds Against.

Napoleon B. Broward

The race, expected to be an exciting showdown, proved to be such a bore that election news was pushed off the front page by coverage of Halley's Comet.

New College Lane

Just beyond to the east on the north side of the lane is a terraced house that was occupied by Edmund Halley, after whom Halley's Comet is named.

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.

Paul de Casteljau

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

Paul Halley

While organist and choirmaster at the Cathedral of St. John the Divine, 1977 to 1989, he collaborated with Paul Winter to create the Missa Gaia/Earth Mass, Halley became a member of the Paul Winter Consort, and earned five Grammy Awards for his contributions as a composer and performer with the group.

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.

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.

Southern Maryland

Arthur Storer, first astronomer in the American colonies and the original namesake for Halley's Comet, lived the latter part of his life in Calvert County.

St Clears

Nearby Trefenty House became the home of a branch of the Perrot family in the 16th century, and it was here that the amateur astronomer Sir William Lower and a neighbour, John Protheroe, set up one of Britain's first telescopes in 1609, which they used to study the craters of the Moon and Halley's Comet.

Verlet integration

It was also used by Cowell and Crommelin in 1909 to compute the orbit of Halley's Comet, and by Carl Størmer in 1907 to study the motion of electrical particles in a magnetic field.

Victor Halley

Halley soon became closely aligned with Harry Diamond, and in 1944 he was a founder member of the Socialist Republican Party.

Wace

The Roman de Rou also includes a mention of the appearance of Halley's Comet.

Whales Alive

Winter and Halley also collaborate with Leonard Nimoy, who reads poems and prose from various writers, including D.H. Lawrence and Roger Payne.

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.

Zara Yaqob

After witnessing a bright light in the sky (which most historians have identified as Halley's Comet, visible in Ethiopia in 1456), Zara Yaqob founded Debre Berhan and made it his capital for the remainder of his reign.


see also