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searching for Definite matrix 44 found (150 total)

Descent direction (296 words) [view diff] exact match in snippet view article find links to article

gradient method. More generally, if P {\displaystyle P} is a positive definite matrix, then p k = − P ∇ f ( x k ) {\displaystyle p_{k}=-P\nabla f(x_{k})}

Schur product theorem (1,661 words) [view diff] exact match in snippet view article find links to article

Hadamard product of two positive definite matrices is also a positive definite matrix. The result is named after Issai Schur (Schur 1911, p. 14, Theorem

Additive process (2,685 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {R} ^{d}} , A {\displaystyle A} a positive definite matrix in R d × d {\displaystyle \mathbb {R} ^{d\times d}} and ν {\displaystyle

Similarity learning (1,526 words) [view diff] exact match in snippet view article find links to article

symmetric positive definite matrix, D W {\displaystyle D_{W}} is a metric. Moreover, as any symmetric positive semi-definite matrix W ∈ S + d {\displaystyle

Cameron–Martin theorem (1,952 words) [view diff] exact match in snippet view article find links to article

that for a q × q {\displaystyle q\times q} symmetric non-negative definite matrix H ( t ) {\displaystyle H(t)} whose elements H j , k ( t ) {\displaystyle

Symbolic Cholesky decomposition (310 words) [view diff] exact match in snippet view article find links to article

A=(a_{ij})\in \mathbb {K} ^{n\times n}} be a sparse symmetric positive definite matrix with elements from a field K {\displaystyle \mathbb {K} } , which we

Bergman metric (446 words) [view diff] exact match in snippet view article find links to article

called the Bergman distance. The Bergman metric is in fact a positive definite matrix at each point if G is a bounded domain. More importantly, the distance

Gigla Janashia (858 words) [view diff] exact match in snippet view article find links to article

positive definite matrix functions". Studia Mathematica. 137 (1): 93–100. MR 1735630. "On approximate factorization of positive definite matrix functions"

Ellipsoid method (3,705 words) [view diff] exact match in snippet view article find links to article

(a) A vector at a distance of at most ε from K, or -- (b) A positive definite matrix A and a point a such that the ellipsoid E(A,a) contains K, and the

Multivariate stable distribution (1,603 words) [view diff] exact match in snippet view article find links to article

\delta \in R^{d}} (equal to the mean when it exists) and some positive definite matrix Σ {\displaystyle \Sigma } (akin to a correlation matrix, although the

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

only work if f ″ ( x k ) {\displaystyle f''(x_{k})} is a positive definite matrix. While this may seem like a limitation, it is often a useful indicator

Rayleigh quotient (2,803 words) [view diff] exact match in snippet view article find links to article

pre-multiplied by its transpose A ′ {\displaystyle A'} . Being a positive semi-definite matrix, M {\displaystyle M} has non-negative eigenvalues, and orthogonal (or

Sign function (2,790 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\boldsymbol {P}}} is a self-adjoint, or Hermitian, positive definite matrix, both in K n × n {\displaystyle \mathbb {K} ^{n\times n}} . If A {\displaystyle

Hel Braun (564 words) [view diff] exact match in snippet view article find links to article

Harmonic analysis on symmetric spaces—higher rank spaces, positive definite matrix space and generalizations (2nd ed.), New York: Springer-Verlag, p. 424

Harnack's inequality (1,188 words) [view diff] exact match in snippet view article find links to article

x_{i}}}+c(t,x)u} with smooth and bounded coefficients and a positive definite matrix ( a i j ) {\displaystyle (a_{ij})} . Suppose that u ( t , x ) ∈ C 2

Array programming (2,610 words) [view diff] exact match in snippet view article find links to article

Generalized inverse (F*F^(-1)F=F) of a : // symmetric positive semi-definite matrix : I [symmetric] 1 2 3 +-------------------------------------------+

Hyper basis function network (766 words) [view diff] exact match in snippet view article find links to article

Every neuron has an elliptic shape with a varying size. Positive definite matrix, but not diagonal. Training HyperBF networks involves estimation of

Quasi-arithmetic mean (1,936 words) [view diff] exact match in snippet view article find links to article

{\displaystyle F(X)=-\log \det(X)} for X {\displaystyle X} a symmetric positive-definite matrix. The pair of matrix quasi-arithmetic means yields the matrix harmonic

K q-flats (2,218 words) [view diff] exact match in snippet view article find links to article

\left\|x-y\right\|_{A}^{2}=(x-y)^{\mathsf {T}}A(x-y)} where A is a positive semi-definite matrix. If A is the identity matrix, then the Mahalanobis metric is exactly

Reproducing kernel Hilbert space (6,286 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \Gamma } is a symmetric function that is now a positive semi-definite matrix for every x , y {\displaystyle x,y} in X {\displaystyle X} . More formally

Trace (linear algebra) (5,464 words) [view diff] exact match in snippet view article

algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix". Journal of the ACM. 58 (2): 8:1–8:34. doi:10.1145/1944345.1944349

Probability distribution (6,547 words) [view diff] exact match in snippet view article find links to article

beta distribution Wishart distribution, for a symmetric non-negative definite matrix; conjugate to the inverse of the covariance matrix of a multivariate

Gaussian integral (4,300 words) [view diff] exact match in snippet view article find links to article

to the finite-dimensional case. If A is again a symmetric positive-definite matrix, then (assuming all are column vectors) ∫ exp ⁡ ( − 1 2 ∑ i , j = 1

Stochastic approximation (4,388 words) [view diff] exact match in snippet view article find links to article

is a Hurwitz matrix A {\textstyle A} and a symmetric and positive-definite matrix Σ {\textstyle \Sigma } such that { U n ( ⋅ ) } {\textstyle \{U^{n}(\cdot

Kernel methods for vector output (4,218 words) [view diff] exact match in snippet view article find links to article

for the outputs and K {\displaystyle {\textbf {K}}} is a positive definite matrix-valued function with entry ( K ( x , x ′ ) ) d , d ′ {\displaystyle

Regularization perspectives on support vector machines (1,469 words) [view diff] exact match in snippet view article find links to article

be written as an n × n {\displaystyle n\times n} symmetric positive-definite matrix K {\displaystyle \mathbf {K} } . By the representer theorem, f ( x

Uncertainty principle (19,264 words) [view diff] exact match in snippet view article find links to article

is a polynomial of degree (N − d)/2 and A is a real d × d positive definite matrix. This result was stated in Beurling's complete works without proof

Gauss–Markov theorem (4,717 words) [view diff] exact match in snippet view article find links to article

}}\right)-\operatorname {Var} \left({\widehat {\beta }}\right)} is a positive semi-definite matrix for every other linear unbiased estimator β ~ {\displaystyle {\widetilde

Schur complement (2,890 words) [view diff] exact match in snippet view article find links to article

multivariate normal distribution whose covariance is the symmetric positive-definite matrix Σ = [ A B B T C ] , {\displaystyle \Sigma =\left[{\begin{matrix}A&B\\B^{\mathrm

SAMV (algorithm) (1,905 words) [view diff] exact match in snippet view article

{\displaystyle {\bf {r}}_{N}} is bounded by the real symmetric positive definite matrix Cov p Alg ≥ [ S d H C r − 1 S d ] − 1 , {\displaystyle \operatorname

Controllability Gramian (2,170 words) [view diff] exact match in snippet view article find links to article

zero). This makes W c {\displaystyle {\boldsymbol {W}}_{c}} a positive definite matrix. More properties of controllable systems can be found in Chen (1999

Local regression (5,378 words) [view diff] exact match in snippet view article find links to article

Since w {\displaystyle w} is a metric, it is a symmetric, positive-definite matrix and, as such, there is another symmetric matrix h {\displaystyle h}

Observability Gramian (2,149 words) [view diff] exact match in snippet view article find links to article

and that makes W o {\displaystyle {\boldsymbol {W}}_{o}} a positive definite matrix. More properties of observable systems can be found in, as well as

Compressed sensing (5,874 words) [view diff] exact match in snippet view article find links to article

the image, the structure tensor J is a symmetric and positive semi-definite matrix. Convolving all the pixels in the image with G {\displaystyle G} ,

Graph coloring (8,122 words) [view diff] exact match in snippet view article find links to article

Vector chromatic number: Let W {\displaystyle W} be a positive semi-definite matrix such that W i , j ≤ − 1 k − 1 {\displaystyle W_{i,j}\leq -{\tfrac {1}{k-1}}}

Normal distribution (22,601 words) [view diff] exact match in snippet view article find links to article

normal distribution. The variance of X is a k×k symmetric positive-definite matrix V. The multivariate normal distribution is a special case of the elliptical

Legendre transformation (8,906 words) [view diff] exact match in snippet view article find links to article

x,Ax\rangle +c} be defined on X = Rn, where A is a real, positive definite matrix. Then f is convex, and ⟨ p , x ⟩ − f ( x ) = ⟨ p , x ⟩ − ⟨ x , A x

Data-driven control system (2,978 words) [view diff] exact match in snippet view article find links to article

the step size, R i {\displaystyle R_{i}} is an appropriate positive definite matrix and d J ^ d ρ {\displaystyle {\frac {d{\widehat {J}}}{d\rho }}} is

Minimum mean square error (9,310 words) [view diff] exact match in snippet view article find links to article

Since the matrix C Y {\displaystyle C_{Y}} is a symmetric positive definite matrix, W {\displaystyle W} can be solved twice as fast with the Cholesky

Interval finite element (6,448 words) [view diff] exact match in snippet view article find links to article

parameter-dependent system of equations (usually with a symmetric positive definite matrix.) An example of the solution set of general parameter dependent system

List of numerical analysis topics (8,339 words) [view diff] exact match in snippet view article find links to article

decomposition Cholesky decomposition — for solving a system with a positive definite matrix Minimum degree algorithm Symbolic Cholesky decomposition Iterative

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

of these viewpoints. The method depends on 2 parameters: a positive definite matrix B {\displaystyle B} giving rise to a weighted Euclidean inner product

Riemannian connection on a surface (10,191 words) [view diff] exact match in snippet view article find links to article

u i ⋅ u j {\displaystyle g_{ij}=u_{i}\cdot u_{j}} It is a positive-definite matrix. Its inverse is also positive-definite symmetric, with matrix g i j

Stein discrepancy (4,615 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \Sigma \in \mathbb {R} ^{d\times d}} a symmetric positive definite matrix, and if we denote u ( x ) = ∇ log ⁡ p ( x ) {\displaystyle u(x)=\nabla