Then, we modify the original CPM-RID algorithm by directly dividing the parity check matrix into several

submatrices, which can reduce the decoding delay and increase the convergence rate by adapting a certain decoding scheme, like serial mechanism.

According to the low-rank decomposition, the far-field interaction matrix [Z.sub.far] with rank-deficient property can be approximated by a product of two much smaller

submatrices U and V:

(i) Search all triads (which generate all 3 by 3 PC

submatrices) and locate the worst triad with an inconsistency indicator (ii).

They divide the above three matrices into p equally sized

submatrices by column; that is, X = [[X.sub.1], ..., [X.sub.p]], U = [[U.sub.1], ..., [U.sub.p]], and V = [[V.sub.1], ..., [V.sub.p]].

(7), even though proteins can have different 3D shapes, and thus, different contact maps, there are common

submatrices of the distance matrices that can be found in different proteins.

The

submatrices of H can be written as [??], where [U.sub.k] is the principal submatrix of U and [C.sup.(k)] is a companion matrix whose last column is [??] Hence, [H.sub.k] is nonsingular if [U.sub.k.sup.-1] is nonsingular, that is, all the diagonal entries are nonzero.

The SAM also contained

submatrices that described nonmarket income flows.

To do this, we write the matrix Y(s) in the form of four

submatrices as shown in

The construction of QC-LDPC codes relies on an [m.sub.b] x [n.sub.b] matrix [H.sub.b] sometimes called the base matrix which comprises cyclically right-shifted identity and zero

submatrices both of size z x z, where, z [member of] [Z.sup.+], 0 [less than or equal to] [i.sub.b] [less than or equal to] ([m.sub.b] - 1) and 0 [less than or equal to] [j.sub.b] [less than or equal to] ([n.sub.b] - 1), the shift value,

The 1,3,5, and 7 bits in the binary numbers of each pixel are taken out as the low 4 bits of a byte, with a high 4-bit complement 0; then, it forms a byte and rebuilds the

submatrices with new pixel values in the corresponding positions.

Particularly, when M = 3, the

submatrices of a third-order tensor are indeed the frontal slices.