Sometimes it is necessary to roughly calculate the square inch area of the opening but the calculation can usually be made with sufficient accuracy that it won't affect the final computation.

Because and can be very similar numbers, the precision of the result can be much less than the inherent precision of the floating-point arithmetic used to perform the computation.

Likewise, there is a formula for combining the covariances of two sets that can be used to parallelize the computation:

He was highly influential in the development of computer science, giving a formalisation of the concepts of " algorithm " and " computation " with the Turing machine, which can be considered a model of a general purpose computer.

Exact ( not asymptotic ) measures of efficiency can sometimes be computed but they usually require certain assumptions concerning the particular implementation of the algorithm, called model of computation.

For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.

More technically, the law is concerned with the speedup achievable from an improvement to a computation that affects a proportion P of that computation where the improvement has a speedup of S. ( For example, if an improvement can speed up 30 % of the computation, P will be 0. 3 ; if the improvement makes the portion affected twice as fast, S will be 2.

In most cases, the computation is intractable, but good approximations can be obtained using Markov chain Monte Carlo methods.

Although the above recursive formula can be used for computation it is

But it is often more practical in numerical computation to perform the scaling all at once as above ( and a unit scaling can be convenient in other ways ).

If all layers of an image change regularly but a large number of layer still need to be composited ( such as in distributed rendering ), the commutativity of a compositing operator can still be exploited to speed up computation through parallelism even when there is no gain from pre-computation.

Electricity's extraordinary versatility as a means of providing energy means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation.

The difference in speed can be substantial, especially for long data sets where N may be in the thousands or millions — in practice, the computation time can be reduced by several orders of magnitude in such cases, and the improvement is roughly proportional to N / log ( N ).

* Like the quasi-arithmetic means, the computation of the mean can be split into computations of equal sized sub-blocks.

In many other languages, evaluation can be delayed by explicitly suspending the computation using special syntax ( as with Scheme's "" and "" and OCaml's "" and "") or, more generally, by wrapping the expression in a thunk.

Values can come from constants, from computation involving values of other variables, or from the output of a function.

This cycle can be used to predict eclipses, forms the basis of the Greek and Hebrew calendars, and is used in the computation of the date of Easter each year.

Textbooks and scientific publications related to computer science and numerical computation often use pseudocode in description of algorithms, so that all programmers can understand them, even if they do not all know the same programming languages.

Any of these steps can be chosen in a computation.

Major goals of quantum chemistry include increasing the accuracy of the results for small molecular systems, and increasing the size of large molecules that can be processed, which is limited by scaling considerations — the computation time increases as a power of the number of atoms.

If your computation on Form 1040 or Form 1040A shows you owe additional tax, it should be remitted with your return unless you owe less than $1, in which case it is forgiven.

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

Unfortunately there may be a tradeoff between goodness ( speed ) and elegance ( compactness )— an elegant program may take more steps to complete a computation than one less elegant.

It is often useful to be able to compute the variance in a single pass, inspecting each value only once ; for example, when the data are being collected without enough storage to keep all the values, or when costs of memory access dominate those of computation.

This methodology could be used for parallel computation of statistical moments with subsequent combination of those moments, or for combination of statistical moments computed at sequential times.

A model of computation may be defined in terms of an abstract computer, e. g., Turing machine, and / or by postulating that certain operations are executed in unit time.

A key point which is often overlooked is that published lower bounds for problems are often given for a model of computation that is more restricted than the set of operations that you could use in practice and therefore there are algorithms that are faster than what would naively be thought possible.

The running time of the new computation will be the length of time the unimproved fraction takes ( which is 1 − P ), plus the length of time the improved fraction takes.

By working very hard, one may be able to make this part 5 times faster, but this only reduces the time for the whole computation by a little.

With current technology, AI-complete problems cannot be solved by computer alone, but also require human computation.

Plane radios were not yet available, and once in the air, Fogg flew his ship by compass, a good memory for landmarks as seen from above, and a capacity for dead reckoning and quick computation.

The principal advantages of the formalism are that it allows the computation of off-shell amplitudes and, when a classical action is available, gives non-perturbative information that cannot be seen directly from the standard genus expansion of string scattering.

Then this can be seen by a direct computation for n any integer, and the general case reduces to this case without much difficulty.

In addition, CI also embraces biologically inspired algorithms such as swarm intelligence and artificial immune systems which can be seen as a part of evolutionary computation.

As can be seen, Monte Carlo Methods are particularly useful in the valuation of options with multiple sources of uncertainty or with complicated features, which would make them difficult to value through a straightforward Black – Scholes-style or lattice based computation.

Aside from written numerals, the first aids to computation were purely mechanical devices which required the operator to set up the initial values of an elementary arithmetic operation, then manipulate the device to obtain the result.

Moreover, since all of these polynomials have purely real coefficients ( until the very last stage ), they automatically exploit the special case where the inputs x < sub > n </ sub > are purely real to save roughly a factor of two in computation and storage.

Besides their efficiency benefits, the inherent referential transparency of functional data structures tends to make purely functional computation more amenable to analysis and optimization, both formal and informal.

Since every value in a purely functional computation is built up out of existing values, it would seem that it is impossible to create a cycle of references.

Ultrasonic flow meters are more complex than meters that are purely mechanical, as they require significant signal processing and computation capabilities.

The Stern-Brocot tree provides an enumeration of all positive rational numbers, in lowest terms, obtained purely by iterative computation of the mediant according to a simple algorithm.