Sentence examples for norm was given from inspiring English sources
In [17], the quaternion matrix equation (1) was considered and the least-squares solution with the least norm was given through the use of the Kronecker product and the Moore-Penrose generalized inverse.
The (original) Morrey space L p, λ ( R N ) with 1 ≤ p < ∞ and 0 < λ ≤ N is a normed space whose norm is given by ∥ f ∥ L p, λ ≡ sup x ∈ R N, r > 0 ( 1 r N − λ ∫ B ( x, r ) | f ( y ) | p d y ) 1 p for f ∈ L loc p ( R N ).
Furthermore a result of asymptotic behavior in uniform norm is given using Benssoussan-Lions' algorithm.
Criteria for nonsquareness and locally uniform nonsquareness of Orlicz-Bochner function spaces equipped with Luxemburg norm are given.
Recall that this norm is given by ∥ A ∥ tr = ∑ j = 1 N σ j ( A ), Open image in new window.
In this paper, criteria for uniform nonsquareness and locally uniform nonsquareness of Orlicz Bochner function spaces equipped with the Orlicz norm are given.
Given a general norm (Vert xVert ) for a real vector x, its dual norm is given by Vert zVert ^=max_{Vert xVert leq 1}z^{T}x.
A P-type ILC scheme is introduced, and a sufficient condition for tracking error convergence in the sense of (mathbf{L}^{2}) norm is given.
The explicit form of the terms in Eq. (14), as well as the details of the computation of the trace norm, are given in Appendix 1.
and its norm is given by y D E C 2 = ∑ n = 1 N u n H r σ n 2 (7).
Both (L_{2}) error norms are given by mathit{L}_{2}= biglVert U^{mathrm{exact}}-U_{N} bigrVert _{2}=sqrt{hsum _{J=0}^{N} biglvert U_{j}^{mathrm{exact}}- ( U_{N} ) _{j} bigrvert ^{2}} and (L_{infty}) error norm is given by mathit{L}_{infty}= biglVert U^{mathrm{exact}}-U_{N} bigrVert _{infty }=max_{j} biglvert U_{j}^{mathrm{exact}}- ( U_{N} ) _{j} bigrvert.
