In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are...

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

mathematics, linearization (British English: linearisation) is finding the linear approximation to a function at a given point. The linear approximation of a...

f(x)=(1+x)^{\alpha }} is a smooth function for x near 0. Thus, standard linear approximation tools from calculus apply: one has f ′ ( x ) = α ( 1 + x ) α − 1...

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems...

1 {\displaystyle \,\!n={^{-1}1}} . A linear approximation (solution to the continuity requirement, approximation to the differentiability requirement)...

polynomial is the linear approximation of the function, and the second-order Taylor polynomial is often referred to as the quadratic approximation. There are...

In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have...

function Triangular function An approximation to a known curve can be found by sampling the curve and interpolating linearly between the points. An algorithm...

expansion used in the approximation. The expressions: a zeroth-order approximation, a first-order approximation, a second-order approximation, and so forth are...

is linear with L, which can be deduced from the fact that the partial with respect to (w.r.t.) L does not depend on L. Thus the linear "approximation" turns...

1/ κ {\displaystyle \kappa } [clarify]. Because the linear approximation is only an approximation, α {\displaystyle \alpha } is different for different...

maps y to f(x) + J(x) ⋅ (y – x) is the best linear approximation of f(y) for all points y close to x. The linear map h → J(x) ⋅ h is known as the derivative...

Piecewise linear function Linear approximation Linear interpolation Discontinuous linear map Linear least squares "The term linear function means a linear form...

is known as the shift vector. At each iteration the model is linearized by approximation to a first-order Taylor polynomial expansion about β k {\displaystyle...

quality of data approximation and some penalty terms for the bending of the manifold. The popular initial approximations are generated by linear PCA and Kohonen's...

of all linear functions of output bits, known as its components. The set of Walsh transforms of the components is known as a Linear Approximation Table...

implies that the approximation ratio in the linear programming relaxation might be bad, and it may be better to look for other approximation schemes for that...

In differential geometry, pushforward is a linear approximation of smooth maps (formulating manifold) on tangent spaces. Suppose that φ : M → N {\displaystyle...

piecewise approximation, harmonic balance or other methods. Software such as the PLECS interface to Simulink uses piecewise linear approximation of the equations...

linear circuit matrix can be solved with Gaussian elimination. Software such as the PLECS interface to Simulink uses piecewise-linear approximation of...

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...

the approximation, though not all approximations are polynomial. Common methods of estimating include scalar, linear, hyperbolic and logarithmic. A decimal...

Portisch's new rating is 2635 + 10×(10.5−9.66) = 2643.4. Elo devised a linear approximation to his full system, negating the need for look-up tables of expected...

not necessary; for instance, it could also be a non-linear model compared to its linear approximation. The Bayes factor can be thought of as a Bayesian...

error is necessarily smaller than the error of a linear approximation which selects the M approximation vectors independently of f. Let us sort { | ⟨ f...

the function 2x increases almost linearly from 1.00000 to 1.05946, allowing for a piecewise linear approximation. Thus, although cents represent a logarithmic...

strain, and the strain rate can be quite complicated, although a linear approximation may be adequate in practice if the quantities are sufficiently small...

f ′ ( c ) {\displaystyle f\,'(c)} is the slope of this linear function, and the approximation is: f ( x ) ≈ f ′ ( c ) ( x − c ) + f ( c ) {\displaystyle...

usually derived by using the implicit function theorem to calculate a linear approximation to the system of equations that defines the equilibrium, under the...