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These algorithms build the nested dissection structure of [[??].sub.22] and the null space matrix Z.

A network programming approach in solving Darcy's equations by mixed finite-element methods

This means that the components of null space vectors corresponding to faces with Neumann boundary conditions must be zero.

Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media

The function 1 is also in the null space of I + [K.sup.*], the adjoint of the integral operator in (6.1), which is clearly necessary for solvability.

Randomized methods for rank-deficient linear systems

The metric for user selection is based on the channel component projected onto the null space of the space spanned by the previously selected user channels.

Low-complexity user selection for rate maximization in MIMO broadcast channels with downlink beamforming

The quotient of [M.sup.p] with respect to the null space [I.sup.p] of the semi-norm is therefore a Banach space, which we denote by [[??].sup.p].

Function spaces with bounded [L.sup.p] means and their continuous functionals

If [alpha] is a null space curve with a spacelike principal normal [??], then the following Frenet formulas hold

On the involute-evolute of the pseudonull curve in Minkowski 3-space

[(A).sup.T], [(A).sup.H], [parallel]A[parallel][sub.2], span (A), null (A) and [A.sup.[dagger]] = [A.sup.H] [([AA.sup.H]).sup.-1] indicate transpose, Hermitian, the Frobenius norm, the column space, the null space and the Moore-Penrose inverse matrix of A, respectively.

Interference alignment based transceiver design in OSG mode of HetNets

Assume now that a basis for the null space of H is given by the vectors

Minimal degree rational unimodular interpolation on the unit circle

Secondly, with the assumption that the eavesdropper's Channel State Information (CSI) is known at the transmitters, the authors in [7] designed the relay beamforming vector in the null space of the eavesdropper's channel to eliminate the information leakage to the eavesdropper.

Secure beamforming with artificial noise for two-way relay networks

Let [{[z.sub.i]}.sup.n-m.sub.i=1] be a basis of the null space of B.

Preconditioners for saddle point linear systems with highly singular (1,1) blocks

This paper presents a new combinatorial approach towards constructing a sparse, implicit basis for the null space of a sparse, under-determined matrix A.

Combinatorial algorithms for computing column space bases that have sparse inverses

First, even if these inclusions hold, the null space [Z.sub.h] is not necessarily a subspace of Z and so (4.7) does not follow from (2.8).

Regularization and stabilization of discrete saddle-point variational problems