This algorithm not only evaluates the curve at, but splits the curve into two pieces at, and provides the equations of the two sub-curves in Bézier form.

Given first 12 digits 979-0-9016791-7, the ISMN algorithm evaluates

A proof of x = y is simply the trivial algorithm if x evaluates to the same number that y does ( which is always decidable for natural numbers ), otherwise there is no proof.

PSQM ( Perceptual Speech Quality Measure ) is a computational and modeling algorithm defined in ITU Recommendation ITU-T P. 861 that objectively evaluates and quantifies voice quality of voice-band ( 300-3400 Hz ) speech codecs.

When the heuristic evaluates to zero, A * is equivalent to Dijkstra's algorithm.

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.

If a naive rendering algorithm is used without any filtering, high frequencies in the image function will cause ugly aliasing to be present in the final image.

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

Once the nearest object has been identified, the algorithm will estimate the incoming light at the point of intersection, examine the material properties of the object, and combine this information to calculate the final color of the pixel.

However, improvements were made, and the actual MUSICAM algorithm was not used in the final MPEG-1 Layer II audio standard.

For example, in an algorithm using the variables A and B but not the variable C, there could be a large amount of code that changes C, and it would have no effect on the algorithm itself, allowing it to be changed endlessly and without heed as to what the final product will be.

Instead, a stable algorithm for solving this more general problem can for example be a divide and conquer algorithm where the array is recursively split into two parts for which the sum is calculated respectively, and where these two sums then are summed together to give the final sum.

If the algorithm is implemented using floating-point arithmetic, then α should get the opposite sign as the k-th coordinate of, where is to be the pivot coordinate after which all entries are 0 in matrix As final upper triangular form, to avoid loss of significance.

The VEGAS algorithm, due to G. P. Lepage, is a method for reducing error in Monte Carlo simulations by using a known or approximate probability distribution function to concentrate the search in those areas of the graph that make the greatest contribution to the final integral.

The ToASCII algorithm can fail in several ways ; for example, the final string could exceed the 63-character limit of a DNS name.

In this algorithm, a variation of selection sort, we bring the largest pancake not yet sorted to the top with one flip, and then take it down to its final position with one more, then repeat this for the remaining pancakes.

They can also be used to easily build an optimal selection algorithm, as well as near-sorting algorithms, which are algorithms that place every element near its final position, a situation in which insertion sort is fast.

The final algorithm looks like this:

Ordinary people can learn this algorithm and thus multiply four digit numbers in their head-writing down only the final result.

In extrinsic evolution only the final best solution in the final population of the evolutionary algorithm is physically implemented, whereas with intrinsic evolution every individual in every generation of the EA's population is physically realized and tested.

As the illumination of different parts of the picture varies, advanced photometers measure the light intensity in different parts of the potential picture and use an algorithm to determine the most suitable exposure for the final picture, adapting the algorithm to the type of picture intended ( see Metering mode ).

He has developed an algorithm for deal making for players who reach the final table in Full Tilt Poker's online tournaments.

The final result is an algorithm taking O ( n log n ) time and O ( n ) space.

The site's final tracking using algorithm 1 posted on Election Day, November 2 gave 262 electoral votes to John Kerry and 261 to George W. Bush, with 15 tossups.

(...) the transformation of data, representing discrete dollar amounts, by a machine through a series of mathematical calculations into a final share price, constitutes a practical application of a mathematical algorithm, formula, or calculation, because it produces ' a useful, concrete and tangible result ' -- a final share price momentarily fixed for recording and reporting purposes and even accepted and relied upon by regulatory authorities and in subsequent trades.

One practical routing algorithm is to pick the pin farthest from the center of the board, then use a greedy algorithm to select the next-nearest pin with the same signal name.

In other words, the higher-dimensional, multi-player, n-in-a-row generalization of game of tic-tac-toe cannot end in a draw, no matter how large n is, no matter how many people c are playing, and no matter which player plays each turn, provided only that it is played on a board of sufficiently high dimension H. By a standard strategy stealing argument, one can thus conclude that if two players alternate, then the first player has a winning strategy when H is sufficiently large, though no constructive algorithm for obtaining this strategy is known.

He also simplified the counting rods technique by outlining short cuts in algorithm procedures used on the counting board, an idea expanded on by the mathematician Yang Hui ( 1238 – 1298 ).

The general merge algorithm has a set of pointers p < sub > 0 .. n </ sub > that point to positions in a set of lists L < sub > 0 .. n </ sub >.

Given the rules of any two-person game with a finite number of positions, one can always trivially construct a minimax algorithm that would exhaustively traverse the game tree.

The simplest greedy algorithm places consecutive labels on the map in positions that result in minimal overlap of labels.

* editing of the duration, amplitude, and spatial positions of all sounds ( possibly done by a script or algorithm )

A brute-force substring search algorithm checks all possible positions:

This results in more equal performance for all head positions, as the expected distance from the head is always half the maximum distance, unlike in the standard elevator algorithm where cylinders in the middle will be serviced as much as twice as often as the innermost or outermost cylinders.

The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields " yes " ( or true ) ( more accurately the number b in location B is greater than or equal to the number a in location A ) THEN the algorithm specifies B ← B − A ( meaning the number b − a replaces the old b ).

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.

While there is no generally accepted formal definition of " algorithm ," an informal definition could be " a set of rules that precisely defines a sequence of operations.

" For some people, a program is only an algorithm if it stops eventually ; for others, a program is only an algorithm if it stops before a given number of calculation steps.

A prototypical example of an algorithm is Euclid's algorithm to determine the maximum common divisor of two integers ; an example ( there are others ) is described by the flow chart above and as an example in a later section.

The concept of algorithm is also used to define the notion of decidability.

In logic, the time that an algorithm requires to complete cannot be measured, as it is not apparently related with our customary physical dimension.

Gurevich: "... Turing's informal argument in favor of his thesis justifies a stronger thesis: every algorithm can be simulated by a Turing machine ... according to Savage, an algorithm is a computational process defined by a Turing machine ".

Typically, when an algorithm is associated with processing information, data is read from an input source, written to an output device, and / or stored for further processing.

Stored data is regarded as part of the internal state of the entity performing the algorithm.

Because an algorithm is a precise list of precise steps, the order of computation will always be critical to the functioning of the algorithm.

In computer systems, an algorithm is basically an instance of logic written in software by software developers to be effective for the intended " target " computer ( s ), in order for the target machines to produce output from given input ( perhaps null ).

is the length of time taken to perform the algorithm.

Simulation of an algorithm: computer ( computor ) language: Knuth advises the reader that " the best way to learn an algorithm is to try it.