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searching for Quadratic function 71 found (123 total)

U-quadratic distribution (300 words) [view diff] exact match in snippet view article find links to article

a continuous probability distribution defined by a unique convex quadratic function with lower limit a and upper limit b. f ( x | a , b , α , β ) = α

Nonlinear conjugate gradient method (1,211 words) [view diff] exact match in snippet view article find links to article

generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function f ( x ) {\displaystyle \displaystyle f(x)} f ( x ) = ‖ A x − b ‖ 2

Generalized chi-squared distribution (2,076 words) [view diff] exact match in snippet view article find links to article

(or generalized chi-square distribution) is the distribution of a quadratic function of a multinormal variable (normal vector), or a linear combination

Quadratic probing (884 words) [view diff] no match in snippet view article find links to article

Quadratic probing is an open addressing scheme in computer programming for resolving hash collisions in hash tables. Quadratic probing operates by taking

Molecular vibration (2,830 words) [view diff] exact match in snippet view article find links to article

harmonic motion. In this approximation, the vibrational energy is a quadratic function (parabola) with respect to the atomic displacements and the first

Carlyle circle (1,275 words) [view diff] exact match in snippet view article find links to article

geometric terms without the notion of a Cartesian coordinate system or a quadratic function and its roots: To divide a straight line, whether internally or externally

Catalecticant (456 words) [view diff] exact match in snippet view article find links to article

into notice as an invariant by Mr Boole; and the discriminant of the quadratic function of x, y is identical with its catalecticant, as also with its Hessian

Natural exponential family (2,056 words) [view diff] exact match in snippet view article find links to article

variance function (NEF-QVF) because the variance can be written as a quadratic function of the mean. NEF-QVF are discussed below. Distributions such as the

Open addressing (1,044 words) [view diff] exact match in snippet view article find links to article

probes increases linearly (hence, the indices are described by a quadratic function). Double hashing in which the interval between probes is fixed for

Degrees of freedom (physics and chemistry) (2,348 words) [view diff] exact match in snippet view article

degrees of freedom. These are degrees of freedom that contribute in a quadratic function to the energy of the system. Depending on what one is counting, there

Linear–quadratic regulator (2,101 words) [view diff] exact match in snippet view article find links to article

set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. One of the main results in the theory is

Placement (electronic design automation) (1,994 words) [view diff] exact match in snippet view article

is an early analytical method that models interconnect length by a quadratic function and uses high-performance quadratic optimization techniques. When

Principal quantum number (1,135 words) [view diff] exact match in snippet view article find links to article

described below, the total energy of an electron is a negative inverse quadratic function of the principal quantum number n, leading to degenerate energy levels

Linear model (831 words) [view diff] exact match in snippet view article find links to article

the model means the following: the function to be minimised is a quadratic function of the β j {\displaystyle \beta _{j}} for which minimisation is a

Bregman divergence (4,475 words) [view diff] exact match in snippet view article find links to article

{\displaystyle t} , then f {\displaystyle f} is a quadratic function. Proof idea: For any quadratic function q : S → R {\displaystyle q:S\to \mathbb {R} }

Internal rate of return (5,484 words) [view diff] exact match in snippet view article find links to article

cash flows; the NPV is a quadratic function of 1/(1 + r), where r is the rate of return, or put differently, a quadratic function of the discount rate r/(1 + r);

Sequential minimal optimization (1,009 words) [view diff] exact match in snippet view article find links to article

solved analytically: one needs to find a minimum of a one-dimensional quadratic function. k {\displaystyle k} is the negative of the sum over the rest of terms

Newton's method in optimization (1,857 words) [view diff] exact match in snippet view article find links to article

point), see below. Note that if f {\displaystyle f} happens to be a quadratic function, then the exact extremum is found in one step. The above iterative

Consistent estimator (1,546 words) [view diff] exact match in snippet view article find links to article

absolute value (in which case it is known as Markov inequality), or the quadratic function (respectively Chebyshev's inequality). Another useful result is the

Polynomial transformation (1,080 words) [view diff] exact match in snippet view article find links to article

the cubic, Tschirnhaus transformations replace the variable by a quadratic function, thereby making it possible to eliminate two terms, and so can be

Linear complementarity problem (1,753 words) [view diff] exact match in snippet view article find links to article

linear complementarity problem is associated with minimizing the quadratic function f ( z ) = z T ( M z + q ) {\displaystyle f(z)=z^{T}(Mz+q)} subject

Lyapunov equation (1,501 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\dot {x}}=Ax} is globally asymptotically stable. The quadratic function V ( x ) = x T P x {\displaystyle V(x)=x^{T}Px} is a Lyapunov function

Latent heat (2,500 words) [view diff] exact match in snippet view article find links to article

−40 °C to 0 °C and can be approximated by the following empirical quadratic function: L ice ( T ) ≈ ( 2834.1 − 0.29 T − 0.004 T 2 ) J/g . {\displaystyle

Derivation of the conjugate gradient method (4,964 words) [view diff] exact match in snippet view article find links to article

of the conjugate direction method applied to minimization of the quadratic function f ( x ) = x T A x − 2 b T x . {\displaystyle f({\boldsymbol {x}})={\boldsymbol

Portfolio optimization (2,702 words) [view diff] exact match in snippet view article find links to article

Analysis 7, 1851–1872. Markowitz, Harry (1956). "The optimization of a quadratic function subject to linear constraints". Naval Research Logistics Quarterly

The Analyst (2,065 words) [view diff] exact match in snippet view article find links to article

circularity. Namely, Berkeley's determination of the derivative of the quadratic function relies on Apollonius's determination of the tangent of the parabola

Convex optimization (3,124 words) [view diff] exact match in snippet view article find links to article

the constraints are all linear, but the objective may be a convex quadratic function. Second order cone programming are more general. Semidefinite programming

Best, worst and average case (1,273 words) [view diff] exact match in snippet view article find links to article

j/2. Working out the resulting average-case running time yields a quadratic function of the input size, just like the worst-case running time. Quicksort

Néron–Tate height (1,802 words) [view diff] exact match in snippet view article find links to article

[-1]^{*}L}(P)+{\frac {1}{2}}{\hat {h}}_{L\otimes [-1]^{*}L^{-1}}(P)} is the unique quadratic function satisfying h ^ L ( P ) = h L ( P ) + O ( 1 ) and h ^ L ( 0 ) = 0.

Overfitting (2,835 words) [view diff] exact match in snippet view article find links to article

slopes). Replacing this simple function with a new, more complex quadratic function, or with a new, more complex linear function on more than two independent

Stress majorization (1,171 words) [view diff] exact match in snippet view article find links to article

Cauchy-Schwarz inequality, see Borg (pp. 152–153). Thus, we have a simple quadratic function τ ( X , Z ) {\displaystyle \tau (X,Z)} that majorizes stress: σ (

Mathematical optimization (6,175 words) [view diff] exact match in snippet view article find links to article

interior-point methods. More generally, if the objective function is not a quadratic function, then many optimization methods use other methods to ensure that some

Multiplicative function (3,445 words) [view diff] exact match in snippet view article find links to article

the divisor function σ k ( n ) {\displaystyle \sigma _{k}(n)} is a quadratic function. Completely multiplicative functions are rational arithmetical functions

Gradient descent (5,398 words) [view diff] exact match in snippet view article find links to article

symmetric and positive-definite, an objective function is defined as the quadratic function, with minimization of F ( x ) = x T A x − 2 x T b , {\displaystyle

Ultrashort pulse (3,346 words) [view diff] exact match in snippet view article find links to article

bandwidth-limited pulse, or where ϕ ( ω ) {\displaystyle \phi (\omega )} is a quadratic function, in which case the pulse is called a chirped pulse because of the

J-structure (1,449 words) [view diff] exact match in snippet view article find links to article

Then (V,j,e) is a J-structure. Let Q be the usual sum of squares quadratic function on Kr for fixed integer r, equipped with the standard basis e1,..

Sphere–cylinder intersection (1,053 words) [view diff] exact match in snippet view article find links to article

{\displaystyle z^{2}+(r^{2}-R^{2}+a^{2})=2ax.} Since x {\displaystyle x} is a quadratic function of z {\displaystyle z} , the projection of the intersection onto the

Preconditioner (3,511 words) [view diff] exact match in snippet view article find links to article

on the figure, which speeds up the convergence. The minimum of a quadratic function F ( x ) = 1 2 x T A x − x T b , {\displaystyle F(\mathbf {x} )={\tfrac

Inverse-variance weighting (1,515 words) [view diff] exact match in snippet view article find links to article

the second partial derivative test by noting that the variance is a quadratic function of the weights. Thus, the minimum variance of the estimator is then

Tait equation (1,887 words) [view diff] exact match in snippet view article find links to article

formula for the instantaneous tangent bulk modulus of pure water is a quadratic function of P {\displaystyle P} (for an alternative see ) K = − V ∂ P ∂ V =

Least squares (5,702 words) [view diff] exact match in snippet view article find links to article

The result of fitting a set of data points with a quadratic function

Matrix representation of conic sections (3,254 words) [view diff] exact match in snippet view article find links to article

center, which can be shown to be the point where the gradient of the quadratic function Q vanishes—that is, ∇ Q = [ ∂ Q ∂ x , ∂ Q ∂ y ] = [ 0 , 0 ] . {\displaystyle

Linear least squares (5,374 words) [view diff] exact match in snippet view article find links to article

The result of fitting a quadratic function y = β 1 + β 2 x + β 3 x 2 {\displaystyle y=\beta _{1}+\beta _{2}x+\beta _{3}x^{2}\,} (in blue) through a set

Modern portfolio theory (7,875 words) [view diff] case mismatch in snippet view article find links to article

slide 6 here Markowitz, H.M. (March 1956). "The Optimization of a Quadratic Function Subject to Linear Constraints". Naval Research Logistics Quarterly

Integral (9,283 words) [view diff] exact match in snippet view article find links to article

further: Simpson's rule approximates the integrand by a piecewise quadratic function. Riemann sums, the trapezoidal rule, and Simpson's rule are examples

Least mean squares filter (3,045 words) [view diff] exact match in snippet view article find links to article

error. The mean-square error as a function of filter weights is a quadratic function which means it has only one extremum, that minimizes the mean-square

Gini coefficient (10,898 words) [view diff] exact match in snippet view article find links to article

approximate the area B, such as approximating the Lorenz curve with a quadratic function across pairs of intervals or building an appropriately smooth approximation

Infrastructure (number theory) (2,490 words) [view diff] exact match in snippet view article

1999, S. Paulus and H.-G. Rück related the infrastructure of a real quadratic function field to the divisor class group. This connection can be generalized

Multivariate t-distribution (5,719 words) [view diff] exact match in snippet view article find links to article

{\displaystyle t_{i}} that replaces t 2 {\displaystyle t^{2}} by a quadratic function of all the t i {\displaystyle t_{i}} . It is clear that this only

Support vector machine (9,064 words) [view diff] exact match in snippet view article find links to article

called the dual problem. Since the dual maximization problem is a quadratic function of the c i {\displaystyle c_{i}} subject to linear constraints, it

Hamiltonian mechanics (9,323 words) [view diff] exact match in snippet view article find links to article

{q}},{\boldsymbol {\dot {q}}})} T {\displaystyle T} is a homogeneous quadratic function in q ˙ {\displaystyle {\boldsymbol {\dot {q}}}} Regarding extensions

Ordinary least squares (9,129 words) [view diff] exact match in snippet view article find links to article

suggests that the relationship is strong and can be approximated as a quadratic function. OLS can handle non-linear relationships by introducing the regressor

Gaussian adaptation (3,037 words) [view diff] case mismatch in snippet view article find links to article

Discrete Optimization of Digital Filters Using Gaussian Adaptation and Quadratic Function Minimization. IEEE Trans. on Circ. and Syst., vol. CAS-34, no 10,

HHL algorithm (4,990 words) [view diff] exact match in snippet view article find links to article

in O ( N s κ ) {\displaystyle O(Ns\kappa )} time by minimizing the quadratic function | A x → − b → | 2 {\displaystyle |A{\vec {x}}-{\vec {b}}|^{2}} . When

Minflux (1,842 words) [view diff] exact match in snippet view article find links to article

position r → {\displaystyle {\vec {r}}} can be approximated by a quadratic function. Therefore, the recorded number of emission photons is: n ( r → ,

Quadratic pseudo-Boolean optimization (1,967 words) [view diff] exact match in snippet view article find links to article

exist. It is always possible to reduce a higher-order function to a quadratic function which is equivalent with respect to the optimisation, problem known

Polynomial ring (8,697 words) [view diff] exact match in snippet view article find links to article

algorithms are efficient, as their computational complexity is a quadratic function of the input size. The situation is completely different for factorization:

Normal distribution (22,597 words) [view diff] exact match in snippet view article find links to article

+Y_{m}^{2}\right)/m}}\sim F_{n,m}.} A quadratic form of a normal vector, i.e. a quadratic function q = ∑ x i 2 + ∑ x j + c {\textstyle q=\sum x_{i}^{2}+\sum x_{j}+c}

Bumblebee models (3,252 words) [view diff] exact match in snippet view article find links to article

spacelike. One commonly used example for the potential is a smooth quadratic function, V = 1 2 κ ( B μ B μ ∓ b 2 ) 2 , {\displaystyle V={\frac {1}{2}}\kappa

Discrete global grid (3,199 words) [view diff] exact match in snippet view article find links to article

object: cube projection: spherical projections in each cube face using quadratic function semi-regular tiles: quadrilateral projections granularity: fine

Riemann hypothesis (16,749 words) [view diff] no match in snippet view article find links to article

Hecke eigenforms. Artin (1924) introduced global zeta functions of (quadratic) function fields and conjectured an analogue of the Riemann hypothesis for

Cayley–Menger determinant (4,617 words) [view diff] exact match in snippet view article find links to article

r^{2}\\r^{2}\\\vdots \\r^{2}\\1\end{matrix}}\right)=0\,.} It is a quadratic function of r2. For example, when n = 2 {\displaystyle n=2} , this gives the

Lasso (statistics) (8,045 words) [view diff] exact match in snippet view article

An example of a PQSQ (piece-wise quadratic function of subquadratic growth) potential function u ( x ) {\displaystyle u(x)} ; here the majorant function

Barzilai-Borwein method (1,318 words) [view diff] exact match in snippet view article find links to article

successful convergence toward the solution. If f {\displaystyle f} is a quadratic function with Hessian A {\displaystyle A} , 1 / α L O N G {\displaystyle 1/\alpha

Kaczmarz method (4,842 words) [view diff] exact match in snippet view article find links to article

(with a very special stepsize) for minimizing the strongly convex quadratic function f ( x ) = 1 2 x T A x − b T x . {\displaystyle f(x)={\tfrac {1}{2}}x^{T}Ax-b^{T}x

Creep and shrinkage of concrete (4,305 words) [view diff] exact match in snippet view article find links to article

in these pores. The rate of bond breakages may be assumed to be a quadratic function of the level of microprestress, which requires Eq. (4) to be generalized

Differential geometry of surfaces (17,594 words) [view diff] exact match in snippet view article find links to article

from S to the tangent plane to S at p; in particular it gives the quadratic function which best approximates this length. This thinking can be made precise

2-satisfiability (9,112 words) [view diff] exact match in snippet view article find links to article

the number of clauses in the instance, which is upper bounded by a quadratic function of the number of variables. Even, Itai & Shamir (1976) describe a

Graph cut optimization (4,232 words) [view diff] exact match in snippet view article find links to article

graph representing the entire function. The graph representing a quadratic function of n {\displaystyle n} variables contains n + 2 {\displaystyle n+2}

Symmetry of diatomic molecules (7,820 words) [view diff] exact match in snippet view article find links to article

}^{Q}}} corresponding to the lines in this branch are given by a quadratic function of ℑ {\displaystyle \Im } if B v {\displaystyle {{B}_{v}}} and B v

Adaptive noise cancelling (4,165 words) [view diff] exact match in snippet view article find links to article

weight inputs so y(t) = X(t)TW. The above expression shows ξ to be a quadratic function of the weight vector W, a multi-dimensional paraboloid with a single