This algorithm is often more numerically reliable than the naïve algorithm for large sets of data, although it can be worse if much of the data is very close to but not precisely equal to the mean and some are quite far away from it.

The dot-com bubble burst, numerically, on Friday, March 10, 2000, when the technology heavy NASDAQ Composite index, peaked at 5, 048. 62 ( intra-day peak 5, 132. 52 ), more than double its value just a year before.

The HDL form is more suited to work with large structures because it's possible to just specify them numerically rather than having to draw every piece by hand.

However, they are either numerically insignificant ( Ainu ), their difference is not as pronounced ( though Ryukyuan culture is closely related to Japanese culture, it is nonetheless distinctive in that it historically received much more influence from China and has separate political and nonpolitical and religious traditions ) or well assimilated ( Zainichi population is collapsing due to assimilation / naturalisation ).

The bonus numerically decreases as the number of cards increases ( and vice-versa ), meaning that when there are more tricks available in a round ( and thereby a greater chance of successfully achieving the bid ), there are less bonus points on offer.

An effective alternative is the singular value decomposition ( SVD ), but there are other less expensive choices, such as QR decomposition with pivoting ( so-called rank-revealing QR factorization ), which are still more numerically robust than Gaussian elimination.

The Coalition intended this force to have overwhelming numbers against the numerically inferior imperial French army — which in fact never came close to reaching Napoleon's goal of more than 2. 5 million under arms.

Halley's Comet has probably been in its current orbit for 16, 000 – 200, 000 years, although it is not possible to numerically integrate its orbit for more than a few tens of apparitions, and close approaches before 837 CE can only be verified from recorded observations.

Although Strabo cited the antique Greek astronomers Eratosthenes and Hipparchus, acknowledging their astronomical and mathematical efforts towards geography, he claimed that a descriptive approach was more practical, such that his works were designed for statesmen who were more anthropologically than numerically concerned with the character of countries and regions.

Although, numerically, Griffith appeared in more episodes portraying Sheriff Andy Taylor in The Andy Griffith Show, he logged more on-screen time as Ben Matlock due to the length of each show.

The allied Greek land forces, which Herodotus states numbered no more than 4, 200 men, had chosen Thermopylae to block the advance of the vastly numerically superior Persian army.

This column was numerically superior to the enemy, but it moved in mass in an intersected country, did not cover its flanks, and its operations having, contrary to order, been commenced long before daylight, its fire was probably more destructive to itself than to the enemy.

In 1945, farms larger than 10 hectares, representing numerically a mere 3 % of all farms in the country, managed 27 % of agricultural land and just seven large estates ( out of 155, 000 farms ) controlled 4 % of agricultural land, averaging more than 2, 000 hectares each ( compared to the average farm size of 2. 5 hectares at that time ).

Compared to rotation matrices they are more numerically stable and may be more efficient.

The Blahut – Arimoto algorithm, co-invented by Richard Blahut, is an elegant iterative technique for numerically obtaining rate – distortion functions of arbitrary finite input / output alphabet sources and much work has been done to extend it to more general problem instances.

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

The number of additions and multiplications required is about twice that of using the LU solver, but no more digits are required in inexact arithmetic because the QR decomposition is numerically stable.

While this does not compare to U. S. cities like San Francisco or New York, early in the 20th century Mexicali was numerically and culturally more Chinese than Mexican.

This time the Assyrian forces of 20, 000 men were numerically so superior that most of Judah's men left the field of battle and advised their leader to do likewise and to await a more favorable opportunity.

The reason for the choice of silver eagles over gold ones is thought to be one of economy ; there were more cavalry and artillery colonels than infantry so it was cheaper to replace the numerically fewer gold ones.

which is numerically equal to the more traditional thermodynamic equilibrium constant written as:

Rather than putting their trust in ephemeral sensations they seek form in the stable relationships of pure design, which symbolize an order more real than the disorder of the perceptual world.

And irrespective of the outcome in centuries elapsed since splitting, calculations obviously carry more concordant and comparable meaning if they deal with the most stable units than with variously unstable ones.

but very few seemed aware that such acceptance and identification need to be supplemented with more enduring and stable identification of and with one's self.

Due to the averaging it is far more stable than any clock would be alone ( see signal averaging for a discussion ).

In 1875 Nobel invented gelignite, more stable and powerful than dynamite, and in 1887 patented ballistite, a forerunner of cordite.

Gelignite was more stable, transportable and conveniently formed to fit into bored holes, like those used in drilling and mining, than the previously used compounds and was adopted as the standard technology for mining in the Age of Engineering bringing Nobel a great amount of financial success, though at a significant cost to his health.

Above this temperature and in ambient light, this metastable allotrope transforms into the more stable black allotrope.

For substances which have two ( or more ) stable crystalline forms, such as diamond and graphite for carbon, there is a kind of " chemical degeneracy ".

Perfect crystals never occur in practice ; imperfections, and even entire amorphous materials, simply get " frozen in " at low temperatures, so transitions to more stable states do not occur.

Current hypotheses suggest that asexual reproduction may have short term benefits when rapid population growth is important or in stable environments, while sexual reproduction offers a net advantage by allowing more rapid generation of genetic diversity, allowing adaptation to changing environments.

Alkenes are relatively stable compounds, but are more reactive than alkanes due to the presence of a carbon-carbon pi-bond.

Although the permanency of acrylics is sometimes debated by conservators, they appear more stable than oil paints.

He particularly criticized the Indo-European languages for promoting a mistaken essentialist world view, which had been disproved by advances in the sciences, whereas he suggested that other languages dedicated more attention to processes and dynamics rather than stable essences.

As to the α and β phases, they might both coexist at ambient conditions with the β phase being more stable.

DNA with high GC-content is more stable than DNA with low GC-content, but, contrary to popular belief, the hydrogen bonds do not stabilize the DNA significantly, and stabilization is mainly due to stacking interactions.

They were partly correct: a white dwarf slightly more massive than the Chandrasekhar limit will collapse into a neutron star, which is itself stable because of the Pauli exclusion principle.

Thus, at a given angular rate of rotation, a concave surface represents the stable situation, and the more rapid the rotation, the more concave this surface.

Bistability as applied in the design of mechanical systems is more commonly said to be " over centre " -- that is, work is done on the system to move it just past the peak, at which point the mechanism goes " over centre " to its secondary stable position.

Only in the 18th century did a steady economic and demographic growth begin, an effect of the reforms by Spain's Bourbon dynasty and a more stable situation along the frontier.

Most ( 66 of 94 ) naturally occurring elements have more than one stable isotope.

For example, the reference state for carbon is graphite, because it is more stable than the other allotropes.

Beginning with carbon, elements are produced in stars by buildup from alpha particles ( helium nuclei ), resulting in an alternatingly-larger abundance of elements with even atomic numbers ( these are also more stable ).

Second, and even more importantly, working memory allows information to be integrated over time so that it can generate a stable representation of the world — Gerald Edelman expressed this point vividly by titling one of his books about consciousness The Remembered Present.