Matrix Partition

Abstract

After the introduction in Section 5.1, the concept of admissible blocks is presented in Section 5.2. It will turn out that blocks satisfying this property allow for a good approximation by a low-rank matrix block. For the partition of the matrix into (admissible) blocks, we need a block cluster tree. Its construction starts with the cluster tree T(I) introduced in Section 5.3. The practical generation is discussed in Section 5.4. The block cluster tree T(I×J) (see Section 5.5) can easily be obtained from cluster trees T(I) and T(J). Together, we obtain the admissible partition of the matrix (cf. §5.6), which is the basis of the definition of hierarchical matrices in the next chapter.