Review of Short Phrases and Links|
This Review contains major "Approximation"- related terms, short phrases and links grouped together in the form of Encyclopedia article.
- An approximation is an inexact representation of something that is still close enough to be useful.
- An approximation (represented by the symbol ≈) is an inexact representation of something that is still close enough to be useful.
- The approximation is far more accurate for relatively small values of the parallax error when compared to the parallax.
- The approximation is close to the true variance only in large samples.
- The approximation is known as first-order raytracing or Gaussian optics.
- Spaces between words offer an easy first approximation, but this approximation is not good enough for machine translation (MT), where many word sequences are not translated word-for-word.
- Note that this is only an approximation that holds true when the orbiting body is of considerably lesser mass than the central one.
- This holds true to any (loop) order in perturbation theory, and thus it also holds true to trea level (zero loops), i.e., in the classical approximation.
- Our figures on admission rates are therefore a good approximation of true, diagnosed incidence.
- The approximation involves replacing the true distribution of the data (unknown) with the empirical distribution of the data.
- Derivation of principal components as the best approximation to the data in a linear subspace.
- Apr 01, 2006; Abstract: Here we were concerned with least square approximation by exponential functions for given data.
- We show that the pathwise uniqueness of the solution implies the convergence in the strong sense of the approximation to the solution.
- The most basic principle in approximation theory is this: the smoother the function, the faster the convergence as N - infty.
- E = M + e * sin(M) * (1.0 + e * cos(M)) If e, the eccentricity, is less than about 0.05-0.06, this approximation is sufficiently accurate.
- In the best case, this assumption is only an approximation.
- To achieve this, an assumption known as the paraxial approximation is made.
- This assumption is mathematically exactly correct for a spherically symmetrical object (such as, to a reasonable approximation, a planet).
- As a first approximation (but see next paragraph), this is a good way of steering the incoming beam onto the optic axis of the objective lens.
- Use the lateral magnification formula for the objective lens, and two rough equalities from the diagram to get an approximation for m ob.
- Going beyond the Gross–Pitaevskii (GP) mean-field approximation, we show that bosons can localize and form polygonal-ring-like crystalline patterns.
- A cognitive model is an approximation to animal cognitive processes (predominantly human) for the purposes of comprehension and prediction.
- Hawking radiation is a prediction of this semiclassical approximation.
- Linear regression is optimal linear (mean-square) prediction; we do this because we hope a linear approximation will work well enough over a small range.
- The importance of the Jacobian lies in the fact that it represents the best linear approximation to a differentiable function near a given point.
- If x and y are vectors, then the best linear approximation to the graph of f depends on how f changes in several directions at once.
- For scattering by particles similar to or larger than a wavelength, see Mie theory or Discrete dipole approximation (they apply to Rayleigh regime as well).
- The gradient of a function f from the Euclidean space to at any particular point x 0 in characterizes the best linear approximation to f at x 0.
- If the model is, in fact, AVTD, the approximation in the symplectic numerical scheme should become more accurate as the singularity is approached.
- In all cases of durable state communism, there was some approximation to the Soviet "model".
- In these cases, geometric similitude and the same value of the Froude number in model and prototype produce a good approximation to dynamic similitude.
- The goodness of the bootstrap approximation and the power of some tests in this class for finite sample sizes are investigated by simulation.
- As in all cases in the physical world, the trajectory is always an approximation of a parabola.
- A second-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a parabola.
- A second order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a parabola.
- Figure 2 shows the graph of an approximation to the antiderivative G(x), also truncated to 8 terms.
- Using an approximation with fewer than n 0 terms may result in a very bad approximation.
- A series expansion up to the 5th power in eccentricity gives an approximation to the true anomaly in terms of the mean anomaly.
- For example, it can be used with linear algebra to find the "best fit" linear approximation for a set of points in a domain.
- One expects that the functions S N ƒ approximate the function ƒ, and that the approximation improves as N tends to infinity.
- Cutoffs have a physical motivation in zero energy ontology but it could be an excellent approximation to take them to infinity.
- Many methods have been developed for calculating added mass, typically using the potential flow approximation.
- An algorithm for calculating the Maximum Likelihood estimator is presented, based on data augmentation and stochastic approximation.
- The results indicate that the approximation based on limiting distribution are unsatisfactory unless number of treatments is very large.
- Results are not much better for the second-order approximation to the Euler equation.
- An approximation for the bias of the ML estimator of the AR parameters is also investigated.
- For example, the bias on the error calculated for log x increases as x increases since the expansion to 1+x is a good approximation only when x is small.
- The Hill sphere is but an approximation, and other forces (such as radiation pressure) can make an object deviate from within the sphere.
- To a very rough approximation, the nucleus can be considered a sphere of uniform charge density.
- Forty slices and twenty stacks give quite a good approximation for a sphere.
- In Fig. 5, we display as a function of the parameters R δ the total energies for N = 6 bosons calculated at several levels of approximation.
- Stochastic approximation methods can be used to estimate the parameters.
- We examine the utility of the mean field approximation for the NNBM, and describe how Monte Carlo sampling techniques can be used to learn its parameters.
- Then, the parameters are refined iteratively, that is, the values are obtained by successive approximation.
- It means that the zero P values were replaced by 0.005 for the SSOWH and SDNB test when used with the chi-square approximation procedure.
- If, however, y and z are small, their values will not to a first approximation be altered if the electric and magnetic deflections occur simultaneously.
- It is a good approximation, however, when the wavelength is very small compared with the size of structures with which the light interacts.
- For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N, using a second order approximation.
- The linear approximation of the first order differential can be fitted to a trend of an O(2) polynomial trend in the BGP table size.
- The absolute error is the magnitude of the difference between the exact value and the approximation.
- The difference between reality and simulation includes at least two aspects: approximation and discretization.
- To a first approximation, the modulation rate of a given filter is the difference between the adjacent frequencies processed by that filter.
- However, it obscures the fact that all this talk of virtual states is just an approximation to quantum mechanics, in which energy is conserved at all times.
- Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to quantum mechanics.
- In quantum mechanics, perturbation theory is a set of approximation schemes for describing a complicated quantum system in terms of a simpler one.
- My research interests are in information theory, signal processing, mathematical statistics, approximation theory, optimization and distributed algorithms.
- Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
- Sadegh P., Constrained optimization via stochastic approximation with simultaneous perturbation gradient approximation, Automatica, 33, 1997, 889-892.
- Furthermore, the values in the point table 302 and slope table 304 are defined over a limited range for which the approximation is valid.
- A first-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a straight line with a slope.
- A first order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a straight line with a slope.
- By assuming that the boundary layer is thin, we can make the approximation that the static pressure is constant across the thickness of the boundary layer.
- Each rectangle, by virtue of the Mean Value Theorem, describes an approximation of the curve section it is drawn over.
- One can use the mean value theorem (for real-valued functions of many variables) to see that this does not rely on taking first order approximation.
- Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis.
- The proof is based on a generalization of the Weierstrass approximation theorem to differentiable functions in several variables.
- Proof. It's clear that the sequence of polynomials of best approximation converges to f(x) uniformly (due to Weierstrass approximation theorem).
- But this is true due to a special property of polynomials of best approximation known from Chebyshev alternance theorem.
- The higher order rule is used to compute the best approximation to an integral over a small range.
- Among the Platonic solids, either the dodecahedron or the icosahedron may be seen as the best approximation to the sphere.
- The Icosahedron is the most nearly spherical of all the Platonic Solids, but it is not really all that close an approximation of a sphere.
- This may be the source of the common assumption that the icosahedron is the Platonic solid that gives the closest approximation to the sphere.
- First, they are solving a set of ordinary differential equations that are themselves an approximation to the underlying stochastic kinetics of the system.
- The approach was verified by solving a test problem and its approximation error was analytically estimated for periodized wavelets.
- The flow field is computed by solving a finite volume approximation of the Navier–Stokes equations on moving grids augmented by turbulence models.
- As can be seen, as the number of terms rises, the error of the approximation is reduced in width and energy, but converges to a fixed height.
- To a rough approximation, factoring a number of a certain size and calculating the discrete logarithm of numbers the same size takes the same amount of work.
- A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value.
- Other Alpha max plus beta min algorithm: an approximation of the square-root of the sum of two squares.
- To sum up, on first approximation, in order to predict the case of a subject in Georgian, one must know the Class and Series of the governing verb form.
- If we minimize this sum, we will obtain a good approximation to the data.
- An approximate distribution of this statistic does not seem to be available, so there is no approximation or probability reported.
- However, if the observed statistic had been less extreme, the chi-square approximation would not have worked as well.
- While direct computation of is rather complex, this technique provides a simple approximation by sampling (e.g.,) matrices from.
- In this Electric Dipole approximation, we can make general progress on computation of the matrix element.
- The concept of an ideal gas is an approximation often used in physics and chemistry in order to simplify calculations.
- The calculations are based on the Born-Oppenheimer approximation, and incorporate the effects of the strong interaction through a scattering length approach.
- Newton's law of universal gravitation provide an excellent approximation for most calculations.
- Isaac Newton 's law of Universal Gravitation (1687) was a good approximation of the behaviour of gravity.
- The EFE reduce to Newton's law of gravity by using both the weak-field approximation and the slow-motion approximation.
- Although this approximation is crude, it allowed him to calculate the deflection of light by gravity, and show that it is nonzero.
- General principles of quantum theory; approximation methods; spectra; symmetry laws; theory of scattering.
- As already mentioned, in quantum theory a molecule might be ascribed a definite shape by using the Born-Oppenheimer approximation.
- The approximation to the chi-square distribution breaks down if expected frequencies are too low.
- As long as the expected frequencies are sufficiently large, the chi-square approximation should be adequate for practical purposes.
- Light and Optics The Greeks had applied the methods of geometry to the study of optics, and Ptolemy had a crude approximation to the law of refraction.
- These results are useful in the numerical analysis of the approximation of partial differential equations by spectral methods.
- One of the many things this is useful for is expressing the point-wise error of a numerical approximation in terms of the mesh size.
- The Dirac delta is very useful as an approximation for a tall narrow spike function (an impulse).
- Science > Mathematics > Algebra > Polynomials
- Encyclopedia of Keywords > Information > Error
- Information > Science > Mathematics > Function
- Communication > Translation > Translation Memory > Parallel Texts
* Accurate Approximation
* Approximation Algorithms
* Approximation Error
* Approximation Theory
* Binomial Distribution
* Chi-Square Approximation
* Close Approximation
* Function Approximation
* Geometric Optics
* Good Approximation
* Linear Approximation
* Normal Distribution
* Numerical Approximation
* Numerical Integration
* Paraxial Approximation
* Rational Approximation
* Sample Size
* Static Analysis
* Taylor Series
* Test Statistic
Books about "Approximation" in