These estimates provide an insight into reasonable directions of search for efficient algorithms.

These algorithms need only a few multiplications and additions to calculate each vector.

These can be implemented as analog circuits ( for instance, using a Sallen Key filter topology, a type of active filter ), or as algorithms in digital signal processing systems.

These brute-force algorithms are computationally manageable for n = 8, but would be intractable for problems of n ≥ 20, as 20!

These algorithms model diffuse inter-reflection which is a very important part of global illumination ; however most of these ( excluding radiosity ) also model specular reflection, which makes them more accurate algorithms to solve the lighting equation and provide a more realistically illuminated scene.

These algorithms are numerical approximations to the rendering equation.

These macros are similar to the algorithms in pseudocode typically used in teaching computer science.

These same interpolation formulas nevertheless continue to be used as part of the software algorithms for solving differential equations.

These algorithms take as input a large set of " features " that are generated from the input data.

These algorithms are not practicable for hand written computation, but are available in any Computer algebra system ( see Berlekamp's algorithm for the case in which the coefficients belong to a finite field or the Berlekamp – Zassenhaus algorithm when working over the rational numbers ).

These algorithms compute an estimate of the likely distribution of annihilation events that led to the measured data, based on statistical principles.

These leaves need not be explicit in computer memory — a null child pointer can encode the fact that this child is a leaf — but it simplifies some algorithms for operating on red – black trees if the leaves really are explicit nodes.

These algorithms first convert the SMILES to an internal representation of the molecular structure and do not simply manipulate strings as is sometimes thought.

These techniques are superficially comparable to weather models that show hurricane storm tracks ; each of several algorithms independently models a complex system ( the weather, in this case ) somewhat differently from each of its sister weather algorithms, and the average of all the algorithms ' output is taken to be the most likely " storm track ".

These algorithms do not work if out-of-order execution is utilized on the platform that executes them.

These asymmetric key algorithms allow one key to be made public while retaining the private key in only one location.

These algorithms use data compression to achieve higher throughput.

These algorithms arrange all particles in a tree, a quadtree in the two-dimensional case and an octree in the three-dimensional case.

These two algorithms form the basis for many variations including LZW, LZSS, LZMA and others.

These applications typically employ complex algorithms and data structures and require high performance.

These algorithms usually come in the form of a flowchart, incorporating ' yes / no ' type decisions, making the algorithm easier to memorize.

These things are important to almost all Persians and perhaps most important to the most ordinary.

These are those operating and capital costs found to vary with number of customers regardless, or almost regardless, of power consumption.

These figures indicate that we are losing almost as many as we are receiving into membership.

These colonnades were almost finished in 432 BC and had two wings, the northern one serving as picture gallery.

These represent the most intellectual type of chamber-music of their period, and it is to be regretted that they have remained almost entirely in manuscript, since a careful study of them is indispensable to anyone who wishes to form an adequate idea of Scarlatti's development.

These settlements lasted almost continuously until Nicolas Denys left in 1659.

These areas are often man-made reservoirs or drainages that have been almost entirely monotypic.

These microprocessors were most prominently used in a variety of DEC workstations and servers, which eventually formed the basis for almost all of their mid-to-upper-scale lineup.

These techniques in some respects resemble modern knife fighting, but emphasized thrusting strokes almost exclusively, instead of slashes and cuts.

These two types of action are almost exclusively used by rifles.

These were composed almost entirely of hydrogen and helium, and may have been massive.

These were the first of the Rajput states, a series of kingdoms which managed to survive in some form for almost a millennium, until Indian independence from the British.

These favorable developments, combined with the presence of a large and cheap labour force, laid the foundation for spectacular economic growth that lasted almost uninterrupted until the " Hot Autumn's " massive strikes and social unrest of 1969-70, which then combined with the later 1973 oil crisis and put an abrupt end to the prolonged boom.

These code values can be used in almost any data interchange system to communicate in the following European languages ( with a few exceptions due to missing characters, as noted ):

These rules are almost same as Muay Thai rules:

These guns were the biggest artillery pieces ever fielded by an army during wartime, and weighed almost 1, 344 tons.

These systems have continued to advance, and modern air warfare consists almost entirely of missile firing.

These are available for almost every musical instrument. One common way to mark progress is to have graded examinations, for example from grade 1 ( beginner ) to grade 8 ( ready to enter higher study at music school ).

These plateaus are rather extensive and almost surround several volcanoes in this area.

These extensions use almost identical gestures as Opera.

These models are based on supermini platforms and have different styles depending on markets: Japanese models are more boxy while Europeans have the bonnet and windshield almost parallel.

These dishes are almost always found in Lebanese, Syrian, and Turkish restaurants.

These realizations led to a series of second generation microkernels, which further reduced the complexity of the system and placed almost all functionality in the user space.

These figures are almost certainly CIA World Factbook estimates.