Quadratic and cubic Bézier curves are most common ; higher degree curves are more computationally expensive to evaluate.

, most effort at scaling multicast up to large networks have concentrated on the simpler case of single-source multicast, which seems to be more computationally tractable.

The public key algorithms known thus far are relatively computationally costly compared with most symmetric key algorithms of apparently equivalent security.

The modular exponentiation here is the most computationally expensive part of the signing operation, and it may be computed before the message hash is known.

Furthermore, there is no efficient way to modify a message and its signature to produce a new message with a valid signature, because this is still considered to be computationally infeasible by most cryptographic hash functions ( see collision resistance ).

Consequently, most systems are computationally equivalent.

Multiple sequence alignments are computationally difficult to produce and most formulations of the problem lead to NP-complete combinatorial optimization problems.

The technique of dynamic programming is theoretically applicable to any number of sequences ; however, because it is computationally expensive in both time and memory, it is rarely used for more than three or four sequences in its most basic form.

Collisions between particles are rarely used, as they are computationally expensive and not visually relevant for most simulations.

Thus, many-body theoretical physics most often relies on a set of approximations specific to the problem at hand, and ranks among the most computationally intensive fields of science.

The two most important combinations of these properties are perfectly binding and computationally hiding commitment schemes and computationally binding and perfectly hiding commitment schemes.

The most widely-studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power.

This method is the most computationally intensive, but is particularly useful if the normal equations matrix, X < sup > T </ sup > X, is very ill-conditioned ( i. e. if its condition number multiplied by the machine's relative round-off error is appreciably large ).

However, for the most part, these models are computationally much harder to deal with and harder to use as tools for qualitative analysis.

However, these solutions are neither the most concise ones ( e. g. still remains the need to notationally differentiate overdetermined systems ) nor the most computationally efficient.

In some circumstances, there may exist additional requirements: one may be interested not only in the solution ( and in the fastest or most computationally efficient way to reach it ) but in how it was reached ; e. g. one may want the " simplest " solution (" simplest " in a logical, non computational sense that has to be precisely defined ).

This makes general HJM models computationally intractable for most purposes.

The factorization step is the most computationally expensive step in the algorithm.

There are two leading methods of indexing performed by most commercial EBSD software: triplet voting ; and minimising the ' fit ' between the experimental pattern and a computationally determined orientation.

For an arbitrary response, this involves a computationally expensive time convolution, although in most cases the time response of the medium ( or Dispersion ( optics )) can be adequately and simply modeled using either the recursive convolution ( RC ) technique, the auxiliary differential equation ( ADE ) technique, or the Z-transform technique.

But, because it contains most of the key atmospheric physics of modern GCMs, EdGCM is also used by climate researchers worldwide who would otherwise not have access to the most recent, computationally expensive, versions of GCMs.

Don't think you have to start with the most expensive equipment in the world.

It isn't as expensive as most people believe it to be.

While patent suits are still among the most complex and expensive forms of litigation, these rules have saved litigants uncounted sums of money.

Warhol's works include some of the most expensive paintings ever sold.

The most expensive buses have air conditioning, while the cheaper buses do not.

However, often it is most advantageous for the player selecting to choose to let the more expensive chains remain on the board ( and trade in their stock of the less expensive chain at the 2-to-1 ratio described below ).

At the time it was being developed, a full, reliable connection-oriented protocol like TCP was considered to be too expensive to implement for most of the intended uses of AppleTalk.

He also shot three of the most expensive music videos ever in the history of Dutch Hip Hop and through a management deal with Cilvaringz, performed in 34 countries worldwide.

This was despite the fact that Frankfurt already had most of the required facilities and using Bonn was estimated to be 95 million DM more expensive than using Frankfurt.

It is known that the Brunei's broadband ranging from 512 kbit / s to 1 Mbit / s is one the most expensive in the world.

With an annual production of approximately 960 million bottles, Bordeaux produces large quantities of everyday wine as well as some of the most expensive wines in the world.

The Big Dig was the most expensive highway project in the U. S. and was plagued by escalating costs, scheduling overruns, leaks, design flaws, charges of poor execution and use of substandard materials, criminal arrests, and even four deaths.

The most expensive was the building of the Phase II Silver Line tunnel under Fort Point Channel, done in coordination with Big Dig construction.

According to a 2003 study undertaken by the International Diabetes Federation ( IDF ) on the access to and availability of insulin in its member countries, synthetic ' human ' insulin is considerably more expensive in most countries where both synthetic ' human ' and animal insulin are commercially available: e. g. within European countries the average price of synthetic ' human ' insulin was twice as high as the price of pork insulin.

* List of most expensive coins

By the end of the 20th century, Cambridge had one of the most expensive housing markets in the Northeastern United States.

Somerset County Council is responsible for running the largest and most expensive local services such as education, social services, the library, roads, public transport, trading standards, waste disposal and strategic planning, although fire, police and ambulance services are provided jointly with other authorities through the Devon and Somerset Fire and Rescue Service, Avon and Somerset Constabulary and the South Western Ambulance Service.

Currently cruise missiles are among the most expensive of single-use weapons, up to several million dollars apiece.

The floodlights were said to be the most expensive in Europe at the time as they were so modern.

These three types of armour made up the bulk of the equipment used by soldiers with mail being the most expensive.

Chlorination and boiling are often the least expensive and most effective means of halting transmission.

According to Mercer's 2011 Worldwide Cost of Living Survey, Dublin is the 13th most expensive city in the European Union ( down from 10th in 2010 ) and the 58th most expensive place to live in the world ( down from 42nd in 2010 ).