Sentence examples for norm version of from inspiring English sources

New ingredients in our proof include an integration of Timorin's mixed Hodge Riemann bilinear relation and a mixed norm version of Hörmander's L2-estimate, which also implies a non-compact version of the Khovanskiĭ Teissier inequality.

To the best of our knowledge, there has not been any matrix Euclidean norm version of Kantorovich inequality yet.

We define the efficiencies between OLSE and BLUE by means of the matrix Euclidean norm and prove a matrix Euclidean norm version of the Kantorovich inequality to limit upper or lower bounds of these efficiencies.

In Section 2, we present a matrix spectral norm versions of the Wielandt inequality.

In this article, we use several new matrix norm versions of the Kantorovich inequality involving a nonnegative definite matrix to make the comparison of efficiencies between OLSE and BLUE in a singular linear model.

In this paper, our goal is to make the comparison of efficiencies between OLSE and BLUE in a singular linear model by using matrix norm versions of the Kantorovich inequality involving a nonnegative definite matrix.

By analogy with the work of Vese and Osher, we consider the approximation of G-norm with ℓ 1 norm and the anisotropic version of directional total variation norm.

To this end, in [6] the authors gave an estimate for the upper bound of the Hölder norm a fractal version of the Hilbert transform for domains with d-summable boundary; a geometric notion introduced in [7], which is essential for integration of a form over a fractal boundary.

Ono et al.: In 2014, Ono et al. [22] proposed a cartoon-texture decomposition using the block nuclear norm (an generalized version of [23]) which interprets the texture component as the combination of overlapped and sheared blockwise low-rank matrices in different directions.

According to the generalization bound in statistical learning theory [ 27], we need to minimize the following objective function for a 2-norm soft margin version of SVM (8) minimize w, b 〈 w ⋅ w 〉 + C ∑ i = 1 n ξ i 2 subject to y i (〈 w ⋅ X i 〉 + b ) ≥ 1 − ξ i, i = 1,..., n. in which, slack variable ξ i is introduced when the problem is infeasible.

Under these conditions, D-MUSICAL and D-Capon give very close results: considering D M norm and D C norm the normalized versions of D-MUSICAL and D-Capon, we have: | D M norm − D C norm | D M norm ≃ | D M norm − D C norm | D C norm ≃ 0. 3%% (19).