The approximation error in a data value is the discrepancy between an exact value and some approximation to it. This error can be expressed as an absolute...

approximation error. In applying corrections to the trajectory or course being steered, cybernetics can be seen as the most general approach to error...

conditions are given by the Heaviside step function. The error function and its approximations can be used to estimate results that hold with high probability...

assumption is not quite correct, and introduces some error. To reduce the error in approximation, Frank Yates, an English statistician, suggested a correction...

An approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus...

are approximations of a function, which become generally more accurate as n increases. Taylor's theorem gives quantitative estimates on the error introduced...

Eric W. (2007). "Paraxial Approximation". ScienceWorld. Wolfram Research. Retrieved 15 January 2014. "Paraxial approximation error plot". Wolfram Alpha. Wolfram...

versions of Taylor's theorem, some giving explicit estimates of the approximation error of the function by its Taylor polynomial. Taylor's theorem is named...

thousandth of the radius when using the simplified formula. The approximation error by using the simplified linear formula will increase as the angle...

mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate...

quasi-Monte Carlo method are beneficial in these situations. The approximation error of the quasi-Monte Carlo method is bounded by a term proportional...

operations done with them. This is a form of quantization error. When using approximation equations or algorithms, especially when using finitely many...

characterizing the errors introduced thereby. What is meant by best and simpler will depend on the application. A closely related topic is the approximation of functions...

(2005). Some more approximations can be found at: Error function#Approximation with elementary functions. In particular, small relative error on the whole...

of order of approximation corresponds to the omission of some terms of the series used in the expansion. This affects accuracy. The error usually varies...

undershoot the function values. As more sinusoids are used, this approximation error approaches a limit of about 9% of the jump, though the infinite Fourier...

smaller the angle is, the relative error of these approximations shrinks by two orders of magnitude. The approximation ⁠ cos ⁡ θ ≈ 1 − 1 2 θ 2 {\displaystyle...

Machine epsilon or machine precision is an upper bound on the relative approximation error due to rounding in floating point number systems. This value characterizes...

{\displaystyle a_{i}} s gives a suitable approximation of the square root, with X n {\displaystyle X_{n}} being the approximation error. For example, in the decimal...

from the approximation. An important part of the analysis of any numerical integration method is to study the behavior of the approximation error as a function...

In mathematics, low-rank approximation refers to the process of approximating a given matrix by a matrix of lower rank. More precisely, it is a minimization...

tolerance. Another application is in the computation of approximation errors when the relative error of a measurement is required.[citation needed] Minimum...

Overfitting is directly related to approximation error of the selected function class and the optimization error of the optimization procedure. A function...

the approximation formula are visually indistinguishable and are nearly identical. One of the accompanying figures gives the graph of the error function...

A minimax approximation algorithm (or L∞ approximation or uniform approximation) is a method to find an approximation of a mathematical function that...

{\displaystyle \mu } will involve the asymptotic limit of the ratio of an approximation error term above to an asymptotic order q {\displaystyle q} power of a...

the number of digits after the decimal separator, one can make the approximation errors as small as one wants, when one has a method for computing the new...

measuring the error. In the simplest case this leads to least squares approximation. Approximation theory studies how to find the best approximation to a given...

A successive-approximation ADC is a type of analog-to-digital converter (ADC) that digitizes each sample from a continuous analog waveform using a binary...

f(x)\approx f(0)+f'(0)(x-0)=1+\alpha x.} By Taylor's theorem, the error in this approximation is equal to α ( α − 1 ) x 2 2 ⋅ ( 1 + ζ ) α − 2 {\textstyle {\frac...