English adopted the French very soon afterwards, but it wasn't until the late 19th century that " algorithm " took on the meaning that it has in modern English.

This is a serious problem with Algorithm I and is due to catastrophic cancellation in the subtraction of two similar numbers at the final stage of the algorithm.

In 1954, Martin Davis programmed Presburger's algorithm for a JOHNNIAC vacuum tube computer at the Princeton Institute for Advanced Study.

In fact, any increase or decrease in radiation intensity that is observed to the same extent at all pixels chosen for correction is eliminated by the correction algorithm.

Image showing shock waves from NASA's X-43A hypersonic research vehicle in flight at Mach 7, generated using a computational fluid dynamics algorithm. On September 30, 1935 an exclusive conference was held in Rome with the topic of high velocity flight and the possibility of breaking the sound barrier.

On any given run of the algorithm, it has a probability of at most 1 / 3 that it will give the wrong answer.

If a " weak " character is followed by another " weak " character, the algorithm will look at the first neighbouring " strong " character.

Shannon's work on information theory showed that to achieve so called perfect secrecy, it is necessary for the key length to be at least as large as the message to be transmitted and only used once ( this algorithm is called the One-time pad ).

For this reason cryptologists tend to look at indicators that an algorithm or key length shows signs of potential vulnerability, to move to longer key sizes or more difficult algorithms.

" The general consensus is that these public key algorithms are insecure at any key size if sufficiently large quantum computers capable of running Shor's algorithm become available.

This quest required that the notion of " algorithm " or " effective calculability " be pinned down, at least well enough for the quest to begin.

* CLU comparison at ' 99 bottles of beer ' multi-language demo algorithm site

Developed in the early 1970s at IBM and based on an earlier design by Horst Feistel, the algorithm was submitted to the National Bureau of Standards ( NBS ) following the agency's invitation to propose a candidate for the protection of sensitive, unclassified electronic government data.

As an example, if we have a color depth of 12bits / pixel and an algorithm that compresses at 40x, then BPP equals 0. 3 ( 12 / 40 ).

In 1970 Danny Cohen presented at the " Computer Graphics 1970 " conference in England a linear algorithm for drawing ellipses and circles.

Since the remainders decrease with every step but can never be negative, a remainder r < sub > N </ sub > must eventually equal zero, at which point the algorithm stops.

The most well-known use of the Cooley – Tukey algorithm is to divide the transform into two pieces of size at each step, and is therefore limited to power-of-two sizes, but any factorization can be used in general ( as was known to both Gauss and Cooley / Tukey ).

The Rader-Brenner algorithm ( 1976 ) is a Cooley – Tukey-like factorization but with purely imaginary twiddle factors, reducing multiplications at the cost of increased additions and reduced numerical stability ; it was later superseded by the split-radix variant of Cooley – Tukey ( which achieves the same multiplication count but with fewer additions and without sacrificing accuracy ).

In most cases this scanline algorithm is at least an order of magnitude faster than the per-pixel one.

Some systems cannot be reduced to triangular form, yet still have at least one valid solution: for example, if y had not occurred in and after the first step above, the algorithm would have been unable to reduce the system to triangular form.

which, at the end of the first part ( Gaussian elimination, zeros only under the leading 1 ) of the algorithm, looks like this:

Insertion sort is a simple sorting algorithm that builds the final sorted array ( or list ) one item at a time.

In conjunction with an appropriate codec using MPEG or various manufacturers proprietary algorithms, an ISDN BRI can be used to send stereo bi-directional audio coded at 128 kbit / s with 20 Hz – 20 kHz audio bandwidth, although commonly the G. 722 algorithm is used with a single 64 kbit / s B channel to send much lower latency mono audio at the expense of audio quality.

* While the decision problem is NP-complete the optimization problem is NP-hard, its resolution is at least as difficult as the decision problem, and there is no known polynomial algorithm which can tell, given a solution, whether it is optimal ( which would mean that there is no solution with a larger, thus solving the decision problem NP-complete ).

* Suppose that there is a compression algorithm that transforms every file into a distinct file which is no longer than the original file, and that at least one file will be compressed into something that is shorter than itself.

For some such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise.

: For an example of the simple algorithm " Add m + n " described in all three levels see Algorithm examples.

The design and strength of all key lengths of the AES algorithm ( i. e., 128, 192 and 256 ) are sufficient to protect classified information up to the SECRET level.

This algorithm, for all strings, allows codes as short as allowed by any other algorithm up to an additive constant that depends on the algorithms, but not on the strings themselves.

In all, the Blowfish encryption algorithm will run 521 times to generate all the subkeys-about 4KB of data is processed.

That briefly means that there is no known algorithm that efficiently solves all instances of SAT, and it is generally believed ( but not proven, see P versus NP problem ) that no such algorithm can exist.

Although this problem seems easier, it has been shown that if there is a practical ( randomized polynomial-time ) algorithm to solve this problem, then all problems in NP can be solved just as easily.

After one pair of Bézout coefficients ( x, y ) has been computed ( using extended Euclid or some other algorithm ), all pairs may be found using the formula

In a symmetric key algorithm ( e. g., DES and AES ), the sender and receiver must have a shared key set up in advance and kept secret from all other parties ; the sender uses this key for encryption, and the receiver uses the same key for decryption.

Derivatives of Shor's algorithm are widely conjectured to be effective against all mainstream public-key algorithms including RSA, Diffie-Hellman and elliptic curve cryptography.

However, consider the short but never halting algorithm which systematically lists and runs all possible programs ; whenever one of them halts its probability gets added to the output ( initialized by zero ).

The simplest checksum algorithm is the so-called longitudinal parity check, which breaks the data into " words " with a fixed number n of bits, and then computes the exclusive or of all those words.

A variant of the previous algorithm is to add all the " words " as unsigned binary numbers, discarding any overflow bits, and append the two's complement of the total as the checksum.

A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem.

The algorithm looks for all nodes in the array which are connected to the start node by a path of the target color, and changes them to the replacement color.

There are many ways in which the flood-fill algorithm can be structured, but they all make use of a queue or stack data structure, explicitly or implicitly.

However, if the shape is complex with many features, the algorithm spends a large amount of time tracing the edges of the region trying to ensure that all can be painted.

The algorithm is as follows: eliminate x from all equations below, and then eliminate y from all equations below.

If a large, b-bit number is the product of two primes that are roughly the same size, then no algorithm has been published that can factor in polynomial time, i. e., that can factor it in time O ( b < sup > k </ sup >) for some constant k. There are published algorithms that are faster than O (( 1 + ε )< sup > b </ sup >) for all positive ε, i. e., sub-exponential.

) is NP-complete, thus it is expected that no algorithm can be both correct and fast ( polynomial-time ) on all cases.