For both, FEM leads to symmetric positive definite (SPD) matrices that, depending on the type of discretization and especially on the topology of the nodal connections, may be efficiently solved by either the Preconditioned Conjugate Gradient (PCG) or a direct solver such as the routine MA57 of the Harwell Software Library.
and Γ(n) is a ρn t × n t deterministic matrix that depends only on the channel statistics, such that, (15).
Grape must is a complex chemical matrix that depends on grape variety, ripeness stage, terroir characteristics, climate, and viticultural factors (Ribereau-Gayon et al. [2006]).
This is done by taking the eigenstructure into account of a certain matrix that depends on the random structure of the problem.
The solution involves the decomposition of a matrix that depends only on the geometry of the surface and not on the positions of the charges.
Step 1: We first re-formulate (5) by an equivalent input-output model, in which H is decomposed into a multiplication of multiple matrices including a matrix that depends only on the signature waveform correlation coefficients.
(39) Then, it is formally possible to define a local equilibrium as: psi_{mathrm{eq}} z,t) :=Upsi z,t), (40) where U is a unitary matrix that depends on M.
where ({sigma _{s}^{2}}) is the power of the received signal, h k denotes the k th column of the channel matrix H, and V k is a diagonal matrix that depends on the residual errors of each estimated symbols: textbf{V}_{k} = {sigma_{s}^{2}}e_{k}{e_{k}^{T}} + sumlimits_{i=1,ineq k}^{M}{nu_{i}^{2}}e_{i}{e_{i}^{T}} (16).
This completes the proof for Lemma 1. ■. Proposition 1 is proved in three steps: Step 1: We first re-formulate (5) by an equivalent input-output model, in which H is decomposed into a multiplication of multiple matrices including a matrix that depends only on the signature waveform correlation coefficients.
