Sentence examples for matrix norm by from inspiring English sources

Define a matrix norm by.

Indeed one can take to be the matrix norm induced by the norm on defined by.

Evidently this means that for the matrix norm induced by,.

Let (vert cdot vert) be any Euclidean norm and (Vert cdot Vert) be the matrix norm induced by this vector.

Let (vert xvert _{(cdot)}) be any vector norm (e.g., (:=1,2,infty)) and (Vert (cdot Vert ) be the matrix norm induced by this vector.

For (1 leq p leqinfty), the matrix norm induced by the p-norm, begin{aligned} | mathbf{A} |_{p} := sup_{vec{x} neqvec{0}} frac{| mathbf{A} vec{x} |_{p}}{| vec{x} |_{p}}, end{aligned} is called the matrix p-norm.

To measure the sensitivity of the solution of the P-matrix linear complementarity problem, Chen and Xiang in [5] introduced the following constant for a P-matrix M: beta_{P}(M =max_{din[0,1]^{n}}big| (I-D+DM ^{-1}D bI-D+DM ^{-1}Dre I-D+DM ^{-1}Dis the matrix norm induced big|he vector norm for (p geq1).

Desired properties of the dictionary can be obtained by adding a regularization term such as the element-wise L1 matrix norm as imposed by the LASSO algorithm [41].

For (A: mathbb {R}^{n}to mathbb {R}^{n}), we consider its matrix norm (|A|=max_{|z|=1}|Az|) generated by (|cdot|).

On the other hand, another way to construct the variable stepsize without calculating matrix norm was proposed by Yang in [13], that is, tau_{n} : = frac{rho_{n} }{ Vert {nabla f(x_{n} )} Vert }, (1.4) where ({ {rho_{n} } }) is a sequence of positive real numbers such that sum_{n = 0}^{infty}{rho_{n} = infty}, qquad sum_{n = 0}^{infty}{ rho_{n}^{2} < infty}.

The Frobenius matrix norm is denoted by ‖ M ‖ F = ∑ i ∑ j m i j 2. The transpose of a matrix or vector is denoted by the superscript τ.