Under point wise ordering, a ≤ b in L X if and only if a(x) ≤ b(x) in L for all x∈X.
These four subbands are written back to the external memory in row-wise order.
It is easy to verify that the sign component-wise order ⪯ is a partial order.
A function defined on is called increasing (with respect to the coordinate-wise order relation) if implies that.
The matrix cells of the i th encoder are filled in column-wise order from top left to bottom right.
Let us equip E + ( m 1, m 2 ) with the point-wise order induced by that of the set of all means.
For each i ∈ I, K i ˆ = ∏ j ∈ I, j ≠ i K j is also equipped with the sign component-wise order.
The set of all means can be equipped with a partial ordering, called point-wise order, defined by, m1 ≤ m2 if and only if m1 a, b) ≤ m2 a, b) for every a, b > 0. We write m1 < m2 if and only if m1 a, b) < m2 a, b) for all a, b > 0 with a ≠ b.
K is equipped with a sign component-wise order, i.e., I is divided into two subsets (possibly empty) I + and I −, λ j = ± 1 are allocated to j ∈ I + and j ∈ I − respectively, and for each x = ( x i ) i ∈ I, y = ( y i ) i ∈ I ∈ K, x ⪯ y is defined by λ j x j ≤ λ j y j for each j ∈ I.
Considering that A k is a spares matrix in most cases, without loss of generality, we assume A k has N A N A < N p × N p unknown entries to be estimated and let a vector a k denote all the N A unknown entries as follows: a k ≜ Vec ( A k ) (13). a k ∈ ℂ N A is an N A × 1 column vector formed by stacking all unknown entries of the matrix A k in a row-wise order.
The set of all means can be equipped with a partial ordering, called a point-wise order, defined by m 1 ≤ m 2 if and only if m 1 ( a, b ) ≤ m 2 ( a, b ) for every a, b > 0. We write m 1 < m 2 if and only if m 1 ( a, b ) < m 2 ( a, b ) for all a, b > 0 with a ≠ b.
