Cyclic of index

Definition 3. A square matrix C is cyclic of index 2 [31] if and only if there exists a permutation matrix P such that... 

The quantity o> in (4.11) is called the relaxation factor. We observe that, for CO = 1, this iterative method reduces to the Gauss-Seidel iterative method of (4.8)-(4.8 ). For reasons of brevity, we shall say that a matrix G, which is cyclic of index 2, is consistently ordered [52] if it is the form of (4.10). With the concept of a consistent ordering. Young [52] established the following general relationship between the eigenvalues A of the successive overrelaxation matrix... 

Theorem 3. Let A he a symmetric and positive definite matrix, and let its corresponding Jacobi matrix M he cyclic of index 2 and consistently ordered. Then... 

We remark that, by using the fact that the Jacobi matrix M is cyclic of index 2 and consistently ordered, the inequality of (4.9) can be sharpened to... 

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See also in sourсe #XX -- [ , ]

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