Consequently the Gaussian theory only supplies a convenient method of approximating to reality ; and no constructor would attempt to realize this unattainable ideal.

It introduced the Gaussian gravitational constant, and contained an influential treatment of the method of least squares, a procedure used in all sciences to this day to minimize the impact of measurement error.

Gauss proved the method under the assumption of normally distributed errors ( see Gauss – Markov theorem ; see also Gaussian ).

Many great mathematicians of the past were preoccupied by numerical analysis, as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.

Namely, the matrix is reduced to an upper triangular matrix by using elementary row operations, as in the first part of the Gaussian elimination method, taking care to preserve the sign of its determinant.

There is a direct method of eliminating multiple ( or repeated ) roots from polynomials with exact coefficients ( integers, rational numbers, Gaussian integers or rational complex numbers ).

It contains the first published description in Europe of the Gaussian elimination algorithm, which Rolle called the method of substitution.

Rolle's statement of the method seems not to have been noticed in so far as the lesson for Gaussian elimination that was taught in 18 and 19th century algebra textbooks owes more to Newton than to Rolle.

The method of chapter 7 was not found in Europe until the 13th century, and the method of chapter 8 uses Gaussian elimination before Carl Friedrich Gauss ( 1777 – 1855 ).

In computational chemistry and molecular physics, Gaussian orbitals ( also known as Gaussian type orbitals, GTOs or Gaussians ) are functions used as atomic orbitals in the LCAO method for the computation of electron orbitals in molecules and numerous properties that depend on these.

Thus this method has much in common with the method of kriging in geostatistics and Gaussian process models.

* Carl Friedrich Gauss publishes Theoria motus corporum coelestium in sectionibus conicis solem ambientum in Hamburg, introducing the Gaussian gravitational constant and containing an influential treatment of the least squares method.

Gaussian wavepacket scattering off square well — simulation using pseudo-spectral method

In recent years they write their orbit determination programs in the Python programming language, employing the Gaussian method.

The Marr – Hildreth edge detection method is simple and operates by convolving the image with the Laplacian of the Gaussian function, or, as a fast approximation by Difference of Gaussians.

In other cases, some kind of numerical integration method is needed, either a general method such as Gaussian integration or a Monte Carlo method, or a method specialized to statistical problems such as the Laplace approximation, Gibbs sampling or the EM algorithm.

" Light chasing " is a method similar to Gaussian elimination which always solves the puzzle, although with the possibility of many redundant steps.

Now there are two related linear equations, each with two unknowns, which lets us produce a linear equation with just one variable, by subtracting one from the other ( called the elimination method ):

The easiest way to compute the rank of a matrix A is given by the Gauss elimination method.

This method has zero emissions, so would have significant benefits such as elimination of greenhouse gases and nuclear waste.

It has been estimated that the waste would be halved using this method, since the necessary refrigeration equipment would consume about half the power saved by the elimination of the majority of resistive losses.

One such method was that of assassination, the selective elimination of prominent rival figures.

The Socratic method is a negative method of hypothesis elimination, in that better hypotheses are found by steadily identifying and eliminating those that lead to contradictions.

An alternative to infant diapers is the infant potty training method or elimination communication, a technique that involves sound association, learning an infant ’ s body language, and reacting quickly enough to reach a suitable spot for elimination.

The golden goal or golden point is a method used in association football, field hockey, ice hockey and korfball to decide the winner of games in elimination matches which end in a draw after the end of regulation time.

Chromosome elimination is another method of producing DHs, and involves hybridisation of wheat with maize ( Zea mays L .), followed by auxin treatment and the artificial rescue of the resultant haploid embryos before they naturally abort.

In the late 1990s, a number of relevant professional societies in United States called for elimination of gender verification, including the American Medical Association, stating that the method used was uncertain and ineffective.

Given a desired backbone conformation, side chain packing can be designed using variations of the dead-end elimination algorithm ; however, attempts to design proteins of novel folds have difficulty using this method due to an absence of plausible backbone models.

This method generalizes to systems with additional variables ( see " elimination of variables " below, or the article on elementary algebra.

Shootouts are also a common format for large heads-up multi-table tournaments, although these may feature double or triple elimination instead of the standard single knockout method.

For the Java language, use of the "" keyword can be used to force method inlining ( resulting in elimination of the method call, no dynamic dispatch and the possibility to constant-fold the value-with no code executed at runtime )

In rendering, z-culling is early pixel elimination based on depth, a method that provides an increase in performance when rendering of hidden surfaces is costly.

The method used in this proof can also be used to prove a cut elimination result for Peano arithmetic in a stronger logic than first-order logic, but the consistency proof itself can be carried out in ordinary first-order logic using the axioms of primitive recursive arithmetic and a transfinite induction principle.

One method of inhibiting or ending a strike is firing union members who are striking which can result in elimination of the union.

If the symbolic name or actual address of an index word or electronic switch appears or is included in the operand of an XRELEASE or SRELEASE statement ( see page 101 ), the specified index word or electronic switch will again be made available, regardless of the method by which it was reserved.

This method of rinsing appears to produce maximum cleansing with minimum soil redeposition.

Most frogs identify prey by movement, and vision appears to be the primary method by which the cane toad detects prey ; however, the cane toad can also locate food using its sense of smell.

Gesner's method of purifying the distillation products appears to have been superior to Young's, resulting in a cleaner and better-smelling fuel.

A general procedure ( the chakravala, or " cyclic method ") for solving Pell's equation was finally found by Jayadeva ( cited in the eleventh century ; his work is otherwise lost ); the earliest surviving exposition appears in Bhāskara II's Bīja-gaṇita ( twelfth century ).

One method of starting is to use both index mirror and horizon mirror shades, of sufficient darkness that the sun appears through either as a solid disk and does not hurt the eyes.

* The spectators are misdirected from the performer's method because they are concentrating on the movement of the feet and the space that appears between the feet and the ground.

The woman appears alive to an unusual measure, which Leonardo achieved by his new method not to draw the outlines, " mainly in two features: the corners of the mouth, and the corners of the eyes " ( Gombrich ), as firmly as that had been the use, before ( sfumato ).

When Hofstadter was awarded the 1961 Nobel Prize in Physics, it subsequently appears in the text of his 1961 Nobel Lecture, " The electron-scattering method and its application to the structure of nuclei and nucleons " ( December 11, 1961 ).

This makes the history of the tree-kangaroos particularly convoluted: it appears that the animals were arboreal at some time in the far distant past, moving afterward to the ground — gaining long kangaroo-like feet in the process — before returning to the trees, where they further developed a shortening and broadening of the hind feet and a novel climbing method.

The current trend nevertheless appears to be towards taking full advantage of this fully automated method, despite the tradeoff in efficiency-because it is claimed that it makes programming easier.

According to skeptical author Robert Carroll, the Silva method appears to be based on the work of Roger Wolcott Sperry, but with Silva's own twists in it that is claimed to make it an inaccurate model.

Using the copy-text method, the critic examines the base text and makes corrections ( called emendations ) in places where the base text appears wrong to the critic.

One of the apparent influences from Spanish styles is the espada y daga ( sword and dagger ) method, but some disagree as Filipino espada y daga appears to be distinct from European rapier and dagger techniques ; the stances are different as weapons used in Eskrima are typically shorter than European swords.

Regardless, people continue to be surprised that Clonaid appears to have overcome those problems ; either Clonaid has been extremely lucky in discovering a superior method of cloning, or the company is making false claims.

Notably, the gathering of wild food plants appears to be an efficient alternative method of subsistence in tropical countries, which may play a role in poverty alleviation.

The one-way method, on the other hand, appears neat and efficient to an outside observer.

When Hofstadter was awarded the 1961 Nobel Prize in Physics, it subsequently appears in the text of his 1961 Nobel Lecture, " The electron-scattering method and its application to the structure of nuclei and nucleons " ( December 11, 1961 ).

His cartoons deal at first mainly with social subjects, and are rough and imperfect in execution, but gradually their method gains in power and their subjects become more distinctly political, and by 1849 the artist is strong enough to produce the splendidly humorous national personification which appears in Disraeli Measuring the British Lion.

The bitboard method for holding a board game appears to have been invented in the mid-1950s, by Arthur Samuel and was used in his checkers program.

For the more complicated game of chess, it appears the method was independently rediscovered later by the Kaissa team in the Soviet Union in the late 1960s, although not publicly documented, and again by the authors of the U. S. Northwestern University program " Chess " in the early 1970s, and documented in 1977 in " Chess Skill in Man and Machine ".

Several German textbooks published about 1800 reported that the mistake was first identified by Christlieb Benedikt Funk in 1779, but the construction itself appears to have received little notice until the middle of the twentieth century when tuning theorist J. Murray Barbour presented it as a good method for approximating equal temperament and similar exponentials of small roots, and generalized its underlying mathematical principles.

In the Sōtō school, the " genjo-koan ", or the " koan of everyday life " which " appears naturally in daily life " is emphasized, and shikantaza ( meditation ) or " just sitting ", and the keeping of the precepts is the main method of training.

One method of performing this illusion would be that the magician appears to show several separate and solid rings, but some of the rings are gimmicked.