linear approximation

linear approximation
In mathematics, the process of finding a straight line that closely fits a curve (function) at some location.

Expressed as the linear equation y = ax + b, the values of a and b are chosen so that the line meets the curve at the chosen location, or value of x, and the slope of the line equals the rate of change of the curve (derivative of the function) at that location. For most curves, linear approximations are good only very close to the chosen x. Yet much of the theory of calculus, including the fundamental theorem of calculus and the mean-value theorem for derivatives, is based on such approximations.

* * *


Universalium. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Linear approximation — In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). DefinitionGiven a differentiable function f of one real variable, Taylor s theorem for n =1 states that …   Wikipedia

  • linear approximation — tiesinė aproksimacija statusas T sritis automatika atitikmenys: angl. linear approximation vok. lineare Approximation, f rus. линейная аппроксимация, f pranc. approximation linéaire, f …   Automatikos terminų žodynas

  • linear approximation — tiesinė aproksimacija statusas T sritis fizika atitikmenys: angl. linear approximation vok. lineare Approximation, f rus. линейная аппроксимация, f pranc. approximation linéaire, f …   Fizikos terminų žodynas

  • Linear cryptanalysis — In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two… …   Wikipedia

  • Approximation — An approximation (represented by the symbol ≈) is an inexact representation of something that is still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as… …   Wikipedia

  • Approximation affine — Tangente au point (a, f(a)) En mathématiques, une approximation affine est une approximation d une fonction au voisinage d un point à l aide d une fonction affine. Par exemple, étant donné une fonction dérivable f d une variable réelle …   Wikipédia en Français

  • linear — linearly, adv. /lin ee euhr/, adj. 1. of, consisting of, or using lines: linear design. 2. pertaining to or represented by lines: linear dimensions. 3. extended or arranged in a line: a linear series. 4. involving measurement in one dimension… …   Universalium

  • approximation linéaire — tiesinė aproksimacija statusas T sritis automatika atitikmenys: angl. linear approximation vok. lineare Approximation, f rus. линейная аппроксимация, f pranc. approximation linéaire, f …   Automatikos terminų žodynas

  • approximation linéaire — tiesinė aproksimacija statusas T sritis fizika atitikmenys: angl. linear approximation vok. lineare Approximation, f rus. линейная аппроксимация, f pranc. approximation linéaire, f …   Fizikos terminų žodynas

  • Linear programming — (LP, or linear optimization) is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships.… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”