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algorithm and is
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.

algorithm and taught
One such algorithm is long division, taught to many school children.
It may be considered semi-supervised as the normal class is taught but the algorithm learns to recognize abnormality.
In this system, the algorithm is manually taught the differences between spam and non-spam.
For multiplication, the most straightforward algorithms used for multiplying numbers by hand ( as taught in primary school ) require O ( N < sup > 2 </ sup >) operations, but multiplication algorithms that achieve O ( N log ( N ) log ( log ( N ))) complexity have been devised, such as the Schönhage – Strassen algorithm, based on fast Fourier transforms, and there are also algorithms with slightly worse complexity but with sometimes superior real-world performance for smaller N. The Karatsuba multiplication is such an algorithm.

algorithm and high
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.
In other words, there is an algorithm for a quantum computer ( a quantum algorithm ) that solves the decision problem with high probability and is guaranteed to run in polynomial time.
There is a simple randomized algorithm due to that runs in time where n is the number of clauses and succeeds with high probability to correctly decide 3-Sat.
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.
A good checksum algorithm will yield a different result with high probability when the data is accidentally corrupted ; if the checksums match, the data is very likely to be free of accidental errors.
This algorithm has proven to be very fast and of high quality for hashing purposes ( especially hashing of integer number keys ).
The authors show that this sorting algorithm runs with high probability in O ( n log n ) time.
Real compression algorithm designers accept that streams of high information entropy cannot be compressed, and accordingly, include facilities for detecting and handling this condition.
That algorithm enforces two constraints: children precede their parents and if a class inherits from multiple classes, they are kept in the order specified in the tuple of base classes ( however in this case, some classes high in the inheritance graph may precede classes lower in the graph ).
A learning algorithm has high variance for a particular input if it predicts different output values when trained on different training sets.
But if the learning algorithm is too flexible, it will fit each training data set differently, and hence have high variance.
If the true function is simple, then an " inflexible " learning algorithm with high bias and low variance will be able to learn it from a small amount of data.
But if the true function is highly complex ( e. g., because it involves complex interactions among many different input features and behaves differently in different parts of the input space ), then the function will only be learnable from a very large amount of training data and using a " flexible " learning algorithm with low bias and high variance.
This is because the many " extra " dimensions can confuse the learning algorithm and cause it to have high variance.
When is large, the learning algorithm will have high bias and low variance.
Larry Stockmeyer has proved that for every # P problem P there exists a randomized algorithm using oracle for SAT, which given an instance a of P and ε > 0 returns with high probability a number x such that.
An algorithm that simulates sputtering based on a quantum mechanical treatment including electrons stripping at high energy is implemented in the program TRIM.
* Too high computational complexity of algorithm
A recombination rate that is too high may lead to premature convergence of the genetic algorithm.
SA can also be used within a standard GA algorithm by starting with a relatively high rate of mutation and decreasing it over time along a given schedule.
The flexibility and robustness of the matching algorithm largely determine the performance of the translation memory, although for some applications the recall rate of exact matches can be high enough to justify the 100 %- match approach.
The importance of the CYK algorithm stems from its high efficiency in certain situations.
The algorithm samples from regions where the posterior probability is high and the chains begin to mix in these regions.

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