Meanwhile, its inverse matrix
can be computed as [K.sup.-1] [member of] M ([Z.sub.N]).
MORRISON, Adjustment of an inverse matrix
corresponding to a change in one element of a given matrix, Ann.
Because the traditional greedy pursuit algorithm needs to compute the inverse matrix
of the sensing matrix, this process requires a significant amount of computation time and storage space, resulting in lower reconstruction probability.
This means that the matrix [[parallel][r.sub.ij](x)[parallel].sup.3.sub.1] is invertible and its inverse matrix
with S reduces A(x) to B(x).
where [Q.sub.m.sup.-1] is the inverse matrix
of [Q.sub.m], [H.sub.m.sup.T] is the transpose matrix of [H.sub.m], and [[[H.sub.m.sup.T] [Q.sub.m.sup.-1] [H.sub.m]].sup.-1] is the inverse matrix
of [[[H.sub.m.sup.T] [Q.sub.m.sup.-1] [H.sub.m]]].
To compute the inverse matrix
, [[[alpha]].sub.-1], an eigen-decomposition method is applied to the original shape matrix [alpha].
The use of the left matrix division operator in the GECCA algorithms executes faster than the inverse matrix
method used in CCA algorithm.
In case of (4x4) coefficient matrix in (6), its inverse matrix
is given by
It is noteworthy to mention a family of preconditioners that are based on the physical properties of the problem and more specifically on the idea that inverse matrix
that is approximately represented by the preconditioner is essentially an approximate solution of the electromagnetic problem.
The special solution [??] = [H.sup.-1]T is one of the least-squares solutions of a general linear system H[beta] = T, [H.sup.-1] which is a generalized inverse matrix
To achieve synchronization between systems (16) and (17), we assume that M is an invertible matrix and [M.sup.-]1 its inverse matrix
. Hence, we have the following result.
where [A.sup.(1)T] is a sub-matrix of the matrix [A.sup.T] =[[A.sup.(1)] [A.sup.(2)]] that has an inverse matrix
(corresponds to the sub-matrix [D.sup.(1)] of the flexibility matrix D and to sub-vector [[theta].sup.(1).sub.p]; selection method of the lines for sub-matrix [A.sup.(1)T] is based only on the existence of its inverse matrix