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searching for Linear approximation 146 found (190 total)

alternate case: linear approximation

Boolean function (2,887 words) [view diff] case mismatch in snippet view article find links to article

components. The set of Walsh transforms of the components is known as a Linear Approximation Table (LAT) or correlation matrix; it describes the correlation between

characteristic have a linear approximation defined, and we expect that for each chosen plaintext pair, the probability of the linear approximation holding for one

Software such as the PLECS interface to Simulink uses piecewise-linear approximation of the equations governing the elements of a circuit. The circuit

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

from the equal off-diagonal components of the strain tensor. The linear approximation to the Green-Lagrange strain shows that the small strain tensor is:

almost linearly from 1.00000 to 1.05946, allowing for a piecewise linear approximation. Thus, although cents represent a logarithmic scale, small intervals

In mathematics and physics, a nonlinear partial differential equation is a partial differential equation with nonlinear terms. They describe many different

to the principle of detailed balance and follow from them in the linear approximation near equilibrium. Experimental verifications of the Onsager reciprocal

efficiently solved with a purpose-designed tool. The jackknife is a linear approximation of the bootstrap. The jackknife estimator of a parameter is found

replaced by linear elements whose values are given by the first-order (linear) approximation of their characteristic curve near the bias point. Many of the electrical

Software such as the PLECS interface to Simulink uses piecewise linear approximation of the equations governing the elements of a circuit. The circuit

binary tree search transverses cutting hyper-planes to locate a local linear approximation. ISAT is an alternative to artificial neural networks that is receiving

temperature and α Δ T ≪ 1 {\displaystyle \alpha \Delta T\ll 1} , a linear approximation will be useful in estimating the value R of a property at a temperature

integrator. For FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled. A mathematical model such

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

mathematical journals. Also he wrote two monographs: in 1963 the book Linear Approximation and in 1971, in collaboration with Sol Weintraub, A Book of Splines

In mathematics, the binary logarithm (log2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x,

direction), or when some tolerance criterion is reached. Within a linear approximation, the parameters α {\displaystyle \displaystyle \alpha } and β {\displaystyle

The resulting error is necessarily smaller than the error of a linear approximation which selects the M approximation vectors independently of f. Let

observations. Technically speaking, the problem is to find the best linear approximation to the mean of the Bayesian predictive density, which is why credibility

be linear-elastic or Hookean. Hooke's law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied

floating-point or integer arithmetic. The integer transform uses non-linear approximation of the 9/7 wavelet and it is used in the lossless coding scheme.

Eugene L. Allgower, Stefan Gnutzmann, "An Algorithm for Piecewise Linear Approximation of Implicitly Defined Two-Dimensional Surfaces", SIAM Journal on

improving linear approximations (Matsui 1994). Having obtained a linear approximation of the form: P i 1 ⊕ P i 2 ⊕ ⋯ ⊕ C j 1 ⊕ C j 2 ⊕ ⋯ = K k 1 ⊕ K k

of Klaman's ideas on global stability based on the stability of linear approximation for a cylindrical phase space gave rise to the Viterbi problem on

that eventually diverge away from the x-axis even faster than the linear approximation. This divergence is a specific property of extrapolation methods

{d} -\mathbf {Y{\bar {m}})} } (see also linear least squares). The linear approximation introduces bias into the statistics. Therefore, more caution than

a single value measured at e.g. 50% saturation level, implying a linear approximation of the not perfectly linear photo response non-linearity (PRNL).

linear cryptanalysis and differential cryptanalysis in the form of a Linear approximation table (LAT) or Walsh transform and Difference Distribution Table

Linear approximation of a nonlinear system: classification of 2D fixed point according to the trace and the determinant of the Jacobian matrix (the linearization

359-366. H. Guo, B. Makki, M. -S. Alouini and T. Svensson, "A Semi-Linear Approximation of the First-Order Marcum Q-Function With Application to Predictor

08950404\cdot \mathrm {ERBS} (f)}}}-14678.49} where f is in Hz. Using the linear approximation (Eq.2) for ERB(f) yields: E R B S ( f ) = 21.4 ⋅ log 10 ⁡ ( 1 + 0

that I x {\displaystyle I_{x}} is a scaled and shifted piecewise-linear approximation of log 2 ⁡ ( x ) {\displaystyle \log _{2}(x)} , as illustrated in

polynomial to a linear relationship (the authors noted that the linear approximation was not tested for air temperatures under 68 °F (20 °C) since the

SiTF curve can be used in the method of least squares to find a linear approximation. Given n {\displaystyle n\,} data points ( x i , y i ) {\displaystyle

A function (blue) and a piecewise linear approximation to it (red)

basic assumption in most iterative minimization algorithms. When a linear approximation is valid, the model can directly be used for inference with a generalized

} This Fourier equation can be derived by substituting Fourier’s linear approximation of the heat flux vector, q, as a function of temperature gradient

only changes by ~25% within the troposphere, one may take a (rough) linear approximation of B with T at the relevant wavelengths, and get: d I d l n N ≈ H

mathematically determining a formula to fit multiple data points) will be a linear approximation, straight line with a slope: a polynomial of degree 1. For example:

the non-linear phase, perturbation amplitude is too large for a linear approximation, and non-linear equations are required to describe fluid motions

piecewise approximation and hard_sigmoid, which is a 3-part piecewise linear approximation (output 0, line with slope 0.2, output 1). Curves and Surfaces in

referred to as a sawtooth wave. The sawtooth wave is a convenient linear approximation to the actual waveform, which is exponential for both charge and

64.17, giving a six-digit glass code of 517642. Consequently, a linear approximation for the refractive index dispersion close that wavelength is given

of the law of mass action the reciprocal relations appear in the linear approximation near equilibrium as a consequence of the detailed balance conditions

substituting ϵ {\displaystyle \epsilon } with its constant value yields the linear approximation T v ≈ T ( 1 + 0.608 w ) . {\displaystyle T_{v}\approx T(1+0.608w)

Chapront-Touzé & Francou 2002. These are not constant, so a first-order (linear) approximation of the secular change is provided. Valid for the epoch J2000.0 (1

mainly this concentration ratio, in addition to TRIC ∂F/∂T. In the linear approximation we find: Fnorm=1+(∂F/∂T-ST)ΔT. Due to the linearity of the fluorescence

differentiable). This is equivalent to the existence of the following linear approximation Δ f ( z 0 ) = f ( z 0 + Δ z ) − f ( z 0 ) = f x Δ x + f y Δ y + η

{\displaystyle \chi ^{2}} (chi-squared) values. One approach is to use a linear approximation to the nonlinear model, which may be a close approximation in the

order terms.}}} Hence as a first-order (i.e. linear) approximation, r t = g t − i t {\displaystyle r_{t}=g_{t}-i_{t}} The bundle of

of the overall packet. The notion of group velocity is based on a linear approximation to the dispersion relation ω ( k ) {\displaystyle \omega (k)} near

almost 70%. A better estimate, and the standard method used, is a linear approximation to the function y = x 2 {\displaystyle y=x^{2}} over a small arc

1992, pp. 417–436. Jean-Marc Robert and Godfried T. Toussaint, "Linear approximation of simple objects," Computational Geometry: Theory and Applications

cannot be analysed or predicted by the computation methods (based on linear approximation) normally used by electrical engineers." Roger C. Dugan et al, Electrical

_{*})_{x},\qquad \varphi '(x).} In a sense, the derivative is the best linear approximation to φ {\displaystyle \varphi } near x {\displaystyle x} . Note that

K\left(\sin {\frac {10^{\circ }}{2}}\right)\approx 2.0102{\text{ s}}.} The linear approximation gives 2 π 1  m g ≈ 2.0064  s . {\displaystyle 2\pi {\sqrt {\frac

displacement of x from its natural position, we may replace F by its linear approximation F1 = F′(0) ⋅ (x−x0) at zero displacement. The approximating function

{\textstyle {\frac {1}{2}}\left|{\vec {a}}_{t,{\text{axial}}}\right|} in linear approximation as in Figure 2. The tidal accelerations at the surfaces of planets

Mathematics 35, Springer, 2006. [A1] "An Algorithm for Piecewise Linear Approximation of Implicitly Defined Two-Dimensional Surfaces", Eugene L. Allgower

the permeability of the material. For the displacement field D the linear approximation is usually excellent because for all but the most extreme electric

in general it is simply a map. As this example illustrates, the linear approximation of a functor (on a topological space) is its sheafification, thinking

the Bregman divergence measures the convexity of: the error of the linear approximation of F from q as an approximation of the value at p: D F ( p , q )

(crater) on the Moon. N.A. Kozyrev, Causal or asymmetric mechanics in linear approximation, Pulkovo, 1958 (text available (in Russian)) N.A. Kozyrev, On the

of motion in order to model the Ekman layer flow and fluxes. The linear approximation, the eddy diffusivity equation with an eddy diffusion coefficient

1-form df  is a section of the cotangent bundle, that gives a local linear approximation to  f  in the cotangent space at each point. A vector field V = (v1

CAGD. Natick, MA: A.K. Peters. ISBN 978-1-56881-123-9. Piecewise linear approximation of Bézier curves – description of De Casteljau's algorithm, including

{\displaystyle (0.98058)^{-1}=1.942\%} relative to the EUR. As the linear approximation to the logarithm deteriorates in the size of the change in the exchange

Roberts, F. D. K. (1973). "An improved algorithm for discrete L1 linear approximation". SIAM Journal on Numerical Analysis. 10 (5): 839–848. Bibcode:1973SJNA

or, in some special cases (e.g., Gaussian distribution assuming a linear approximation), even analytically. The formula can also be used to calculate the

polynomial approximation can be used to find an initial estimate. The linear approximation with minimum worst-case absolute error on the interval [ 0.5 , 1

prediction of gravitational radiation was a mathematical artifact of the linear approximation he had employed in 1916. Einstein believed these plane waves would

two kinds of predicted gravitational memory effect: one based on a linear approximation of Einstein's equations, first proposed in 1974 by the Soviet scientists

considered as a vector space over itself, and corresponds to the best linear approximation of a function. If such an operator exists, then it is unique, and

ISSN 2150-8097. S2CID 11359711. Alobaid, Ahmad; Corcho, Oscar (March 2024). "Linear approximation of the quantile–quantile plot for semantic labelling of numeric columns

derivative of f {\displaystyle f} at p {\displaystyle p} as the best linear approximation to f {\displaystyle f} at p {\displaystyle p} ; it has many generalizations

2 Shobu-Ose-Mori piecewise-linear map discrete real 1 piecewise-linear approximation for Pomeau-Manneville Type I map Sinai map - [2][3] Sprott B chaotic

case the polynomial p n , 1 ( x ) {\displaystyle p_{n,1}(x)} is the linear approximation of f {\displaystyle f} around α {\displaystyle \alpha } which is

Graph of f ( x ) = e x {\displaystyle f(x)=e^{x}} (blue) with its linear approximation P 1 ( x ) = 1 + x {\displaystyle P_{1}(x)=1+x} (red) at a = 0. The

|{\boldsymbol {\delta }}_{0}|\to 0} ensures the validity of the linear approximation at any time. For discrete time system (maps or fixed point iterations)

PMID 19244270. Mammano, F.; Nobili, R (1993). "Biophysics of the cochlea: Linear approximation". The Journal of the Acoustical Society of America. 93 (6): 3320–32

eliminate the calcination step entirely. In practical devices, the linear approximation model (above) is accurate only over a limited temperature range.

two-dimensional Euler equations, i.e. in the non-linear case. The stability in linear approximation was already proven by Lord Kelvin in 1887 and more precisely by William

Stewart, James (2008). Calculus (7th ed.). Cengage Learning. p. 942. ISBN 978-0538498845. Folland, Gerald. "Derivatives and Linear Approximation" (PDF).

175–186. E. Lafortune, S. Foo, K. Torrance, and D. Greenberg, Non-linear approximation of reflectance functions. In Turner Whitted, editor, SIGGRAPH 97

unified field theory if quantum mechanics was considered to be a linear approximation for a field theory of inertia expressed in general relativity. Sachs

11-690 Strauss, Leonard (1970), "Almost Sinusoidal Oscillations — the linear approximation", Wave Generation and Shaping (second ed.), McGraw-Hill, pp. 663–720

doi:10.2307/2526708. JSTOR 2526708. Bera, Anil K (1984). "The Use of Linear Approximation to Nonlinear Regression Analysis". Sankhyā. 46 (3): 285–290. JSTOR 25052353

momentum exchange between the flow and the particle rotation. In the linear approximation for this transport of angular momentum, the rate of flow is written:: p

L]} when γ → − ∞ {\displaystyle \gamma \to -\infty } Translog, a linear approximation of CES via a Taylor polynomial about γ = 0 {\displaystyle \gamma

concept of normality generalizes to orthogonality. Tangent is the linear approximation of a spherical or other curved or twisted line of a function. In

is close to the square root, for which a polynomial or piecewise-linear approximation can be used. The time complexity for computing a square root with

points, and contain 50/4 = 12.5 °P of extract. This is simply the linear approximation to the true relationship between SG and °P. However, the above approximation

motion of a viscous liquid in a thin-walled elastic tube. I. The linear approximation for long waves". Philos. Mag. 46 (373): 199–221. doi:10.1080/14786440208520564

Another way of proving the chain rule is to measure the error in the linear approximation determined by the derivative. This proof has the advantage that it

except that it defines q ( t ) {\displaystyle q(t)} as a piecewise linear approximation of the trajectory x ( t ) {\displaystyle x(t)} that updates its trajectory

non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third). They found that the behavior of the system

\partial v_{t}(w_{t})} of v t {\displaystyle v_{t}} is used as a linear approximation to v t {\displaystyle v_{t}} near w t {\displaystyle w_{t}} , leading

because the floating-point format already provides a piecewise linear approximation of a logarithmic curve. Although gamma encoding was developed originally

the residuals are estimated from the random variables and from a linear approximation of the underlying true model, while the true model needs to be provided

11 {\displaystyle y^{+}=11} . That is, before 11 wall units the linear approximation is more accurate and after 11 wall units the logarithmic approximation

so one can think of u h {\displaystyle u_{h}} as of a piecewise-linear approximation to the exact solution u . {\displaystyle u.} By Céa's lemma, there

of approximating a function near a given point using the "best" linear approximation. This approximation, if it exists, is unique and is given by the

de Moivre's illustration of his piecewise linear approximation

depicting the same registration procedure as above, but with piecewise linear approximation of the projection function. Note that it converges much faster.

significant characteristic of metals used as resistive elements is the linear approximation of the resistance versus temperature relationship between 0 and 100 °C

Hence, moving a small amount γ {\displaystyle \gamma } such that the linear approximation remains valid: F m ( x ) = F m − 1 ( x ) − γ ∑ i = 1 n ∇ F m − 1

A function in H 0 1 , {\displaystyle H_{0}^{1},} with zero values at the endpoints (blue) and a piecewise linear approximation (red)

{\displaystyle s_{x},s_{y},s_{z},\ldots } are small enough. Specifically, the linear approximation of f {\displaystyle f} has to be close to f {\displaystyle f} inside

Onsager equations, we must take the thermodynamic forces in the linear approximation near equilibrium: X i = ∑ k ≥ 0 ∂ 2 s ( n ) ∂ n i ∂ n k | n = n ∗

ρvj by a velocity vi is equal to ρvjvj.[dubious – discuss] In the linear approximation that leads to the above acoustic equation, the time average of this

{r_{S}}{2R_{e}}}\right)}{\exp \left(-{\frac {r_{S}}{2R_{e}}}\right)}}} In the linear approximation z = G M R e c 2 − 1 2 G 2 M 2 R e 2 c 4 + … 1 − G M R e c 2 + 1 2

higher order terms of the system size expansion that go beyond the linear approximation. These terms have been used to obtain more accurate moment estimates

favour of using 2SLS, multiplicative models for conditional means, linear approximation of non-linear causal models, models for distribution effects, and

of the velocity gradient ∇v.) The viscous stress tensor is only a linear approximation of the stresses around a point p, and does not account for higher-order

estimate the climate feedbacks within an offline calculation based on a linear approximation Radiative forcing is used to quantify the strengths of different

content had a profound effect on chemistry and biochemistry. In the linear approximation, the effect of isotopic substitution is proportional to the mass

is 1). In some situations such as numerical analysis, a piecewise linear approximation to the identity is desirable. This can be obtained by taking η1 to

applied EPD processes relative to theoretical values. The simple linear approximation applied by Hamaker's law degrades under higher voltages and longer

be sufficiently small to expand the trigonometric function in a linear approximation. The magnification is thereby eliminated as a parameter. In a patent

(lower) trait values may successfully invade. This follows from the linear approximation S r ( m ) ≈ S r ( r ) + S r ′ ( r ) ( m − r ) {\displaystyle S_{r}(m)\approx

derivatives of the component functions. The differential is the best linear approximation of a function F from Rm to Rn. The pushforward is the smooth manifold

parallelogram (right, in red). The Jacobian at a point gives the best linear approximation of the distorted parallelogram near that point (right, in translucent

Onsager relations follow from the principle of detailed balance in the linear approximation near equilibrium. To formulate the principle of semi-detailed balance

point around which sign(f ) = −sign(f")). As a consequence, the linear approximation to f (x), which is used to pick the false position, does not improve

A piecewise linear approximation of the diode characteristic.

( α , β ) {\displaystyle LAT(\alpha ,\beta )} coefficient of the linear approximation table of F should be nonzero): B l ( F ) = min α ≠ 0 , β , L A T

the monopulse ratio is almost linear. In fact, for many systems a linear approximation is good enough. One can also note that the monopulse ratio is continuous

where · denotes the dot product. This equation represents the best linear approximation of the function f at all points x within a neighborhood of a. For

^{*}\mathbf {T} _{V}} is invertible on V {\displaystyle V} . The best linear approximation of f {\displaystyle f} in V {\displaystyle V} is then given by the

except that the dynamics are approximated by linear systems. The linear approximation is important for maintaining a mathematically tractable analysis

 97–104. Doi:10.1007/s10659-009-9200-x Liu, I.-S. (2011): Successive Linear Approximation for Boundary Value Problems of Nonlinear Elasticity in Relative-Descriptional

of games". MTA Mat. Kat. Int. Kozl. 1: 529–540. Sard, A. (1963). Linear Approximation. Mathematical Surveys and Monographs. Vol. 9. American Mathematical

Slutsky equation only applies to infinitesimal price changes, a linear approximation for finite changes is standardly used. If the prices of the two goods

line -- the drag force per charge on single b.p. vs velocity, dotted line -- linear approximation for comparison. (b): same as (a), but in fine scale

non-linear term (quadratic in one test, cubic in another, and a piecewise linear approximation to a cubic in a third). They found that the behavior of the system

have a higher weight than those further from it, such that a local linear approximation to the nonlinear system is reasonable. This localisation ability

using Taylor series. In the simplest case the Taylor series use only linear approximation u i ( p ) ≈ u i ( p 0 ) + ∑ j ∂ u ( p 0 ) ∂ p j Δ p j {\displaystyle

Pejsa was a lucky coincidence making for an exceedingly accurate linear approximation, especially for N's around 0.36. If a retardation coefficient function

{\displaystyle \otimes } is the tensor product. Since we can compute a (linear) approximation to X i ⊗ Y i {\displaystyle X_{i}\otimes Y_{i}} efficiently, we

asymptotically stable fixed point y = 0 {\displaystyle y=0} in the linear approximation. Moreover, f ¯ 1 {\displaystyle {\bar {f}}^{1}} is continuously differentiable

{f} _{t}(t_{n},\mathbf {z} _{n})s)\,ds\qquad } results from the linear approximation, and r ( t n , z n ; h ) = ∫ 0 h e f x ( t n , z n ) ( h − s ) g

4-high mill, as shown in sketch 1. The red line in graph 1 is the linear approximation F = Fd – M ⋅ (S – Sd) or conversely, the screw-down position where

market prices and 4.4 per cent of prices of production, and the linear approximation is within 2 per cent of full prices of production and 8.7 per cent

surface tension and κ is the curvature of the interface, which in a linear approximation is κ = ∇ 2 η = η x x . {\displaystyle \kappa =\nabla ^{2}\eta =\eta

market prices and 4.4 per cent of prices of production, and the linear approximation is within 2 per cent of full prices of production and 8.7 per cent