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References in periodicals archive ?
Similarly, the null space algorithm which we implemented, can be subdivided into three phases: a first symbolic phase where the shortest path tree and the quotient tree are computed, a second phase where the projected Hessian system is solved by the conjugate gradient algorithm, and a final third phase where we compute the pressure.
For large and sparse problems it is important to keep sparsity of the null space basis as much as possible.
We are currently working on the development of robust software for the null space problem that we expect will be competitive with standard approaches such as QR-based schemes [4], inverse iteration [9, 15], or Arnoldi methods [14].
In other words, the metric [r.sub.S,i] measures the amount of power preserved by user i when [h.sub.i] is projected onto the null space of H(S).
We also recall that the null space, [I.sup.p] of the Marcinkiewicz semi-norm, endowed with the norm of [M.sup.p], is a Banach space.
Thus the column vector of [([[bar.V].sub.k,M]).sup.(0)] is an orthogonal basis for the null space of [[bar.H].sub.k,M].
Since we assume that Problem I is damaged we have m' [greater than or equal to] n/2 and k = (n - 1) - m' [less than or equal to] n/2 - 1, so 2(n - k) [greater than or equal to] n + 2 and consequently the null space of N is nontrivial and at least 2-dimensional.
It also shows that, with the increase of [[gamma].sub.E], the infeasibility rate of RBoA decreases from 74% to 40%, while the infeasibility rate of null space based scheme is unchanged with the varying [[gamma].sub.E].
Many applications require a matrix Z that represents a basis for the null space of a large, sparse, under-determined matrix A.
The main idea is to capture the null space of the (curl, curl) operator on each of the coarser levels.
where null (*) denotes an orthonormal basis for the null space of a matrix.
Notably, U can be decomposed into a signal space S and a noise or null space N.