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In numerical mathematics, hierarchical matrices (H-matrices) [1] [2] [3] are used as data-sparse approximations of non-sparse matrices. While a sparse matrix of dimension can be represented efficiently in () units of storage by storing only its non-zero entries, a non-sparse matrix would require () units of storage, and using this type of matrices for large problems would therefore be ...
Jones family worksheet for Maintenance Costs. Plus signs indicate good maintenance history; the more plus signs, the lower the maintenance costs. Even though every column on the worksheet contains a different type of information, the Joneses can use it to make reasonable, rational judgments about Maintenance Costs.
Each colored box in the hierarchy diagram above is called a node. The nodes at each level will be compared, two by two, with respect to their contribution to the nodes above them. The results of these comparisons will be entered into a matrix which is processed mathematically to derive the priorities for all the nodes on the level. [Note 3]
The general principle of hierarchical approximations consists of a repeated application of some other method, such that each consecutive application refines the quality of the approximation. Even though they can be expressed as a set of statistical assumptions, they are often described in terms of a hierarchical matrix approximation (HODLR) or ...
A block-hierarchical matrix. It consist of growing blocks placed along the diagonal, each block is itself a Parisi matrix of a smaller size. In theory of spin-glasses is also known as a replica matrix. Pentadiagonal matrix: A matrix with the only nonzero entries on the main diagonal and the two diagonals just above and below the main one.
The design of any AHP hierarchy will depend not only on the nature of the problem at hand, but also on the knowledge, judgments, values, opinions, needs, wants, etc. of the participants in the decision-making process. Constructing a hierarchy typically involves significant discussion, research, and discovery by those involved.
In theoretical physics, the hierarchy problem is the problem concerning the large discrepancy between aspects of the weak force and gravity. [1] There is no scientific consensus on why, for example, the weak force is 10 24 times stronger than gravity .
Hierarchical; Matrix; Flat (also known as Horizontal) There is no accepted form for making organization charts other than putting the principal official, department or function first, or at the head of the sheet, and the others below, in the order of their rank. The titles of officials and sometimes their names are enclosed in boxes or circles.