Accordingly, we proposed five ridge regression (RR) estimators for the probit regression models for estimating the parameters when the weighted design matrix is ill-conditioned and it is suspected that the parameter β may belong to a linear subspace defined by Hβ="h.
In fact, we can prove that the iterative methods approach the pseudo-inverse (least squares) solution for a noisy environment; specially, when the matrix is ill-conditioned [50].
Although linear precoding techniques have considerably low computational complexity, they show relatively low performance due to the susceptible noise amplification, particularly when the channel matrix is ill-conditioned.
The interferer in Figure 5 is nearly on this line (c = 2) and the related A θ1, θ2) matrix is ill-conditioned as both sources have nearly the same response vector.
Otherwise, the matrix is ill-conditioned so we evaluate (varvec{s}_n) by solving the underdetermined system ([A]^T_{I_n} varvec{s}_n=varvec{y}) using the least squares method which is equivalent to Eq. 13 but does not suffer from ill-conditioning and results in reasonable solutions.
One should bear in mind that the dominating 20 components explain more than 75% of the total variation and that the gene expression matrix is ill-conditioned (condition number above 2000), so the dataset is not sufficiently informative for complete network inference (Nordling, 2013).
Although these methods are rather straightforward, they may not be robust against quantization or additive noise when the matrices are ill conditioned.
Even if the complete data could be analyzed simultaneously, variance component estimation would remain a challenge since the usual estimation methods are very slow or unstable, when the (co variance matrices are ill-conditioned.
As the matrix system is ill conditioned, the collocation technique is preconditioned by a standard Galerkin finite element method using a 9-nodes Lagrangian element which presents decisive advantages: sparsity, reduced condition number, easy treatment of complicated geometries.
From Table 5, we observe that the values of Estep are comparable with those of err, with the exception of the test problems σ u) = σ 1, σ 2, u x, y, t) = u 2 for τ = 10-3, 10-4, where the discrepancy between err and Estep depends on the fact that the matrix A u) is ill conditioned because the Lipschitz constant is large.
