Recently, the diffusion strategy has been used in several applications including sparse system
identification  and multitask networks  where the adaptive network is assigned to perform estimations for more than one desired variable.
Integrating the Bayes model into the RW sparse system
, the organ is automatically segmented for the adjacent slice, which is called RWBayes algorithm in the article.
While direct methods can be applied to solve this kind of system at a much lower cost , iterative methods are very useful for a large sparse system
. But for small or medium sparse matrix, iterative methods cannot do better than direct methods.
Although the SMNLMS algorithm can provide excellent estimation performance, its behavior may be degraded for estimating sparse system
such as sparse multipath wireless communication channel.
The PNLMS algorithm, which is an NLMS algorithm improved by the use of a proportionate technique, has been proposed for sparse system
identification and echo cancellation.
Mei, "??0 norm constraint LMS algorithm for sparse system
identification," IEEE Signal Processing Letters, vol.
Motivated by the proportionate step-size adaptive filtering [13,14], the proportionate NSAF (PNSAF) has been presented to combat poor convergence in sparse system
Just like the other problems, this is the most time-consuming step, that is, to solve the sparse system
Ax = b.
of nonzero entries, N-size of sparse system
of linear equations, T-a mass matrix, S-a stiffness matrix.
Despite the fact that, in this case, A will in general be dense, the problem can still be considered sparse as all linear algebra operations required involve only sparse matrix multiplication, and sparse system
solves as A never needs to be formed to implement the ADI method; see .
The weighted least square method, which involves solving a large and sparse system
of linear equations at every iteration of the state estimation process, is the most widely used.
First of all the zero-attracting LMS (ZA-LMS) and reweighted ZA-LMS (RZA-LMS) algorithms had been proposed in  specially for sparse system
identification and from that time, almost all newly presented sparsity aware algorithms have shared the penalty terms of these algorithms.