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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.
First distance matrix update We then proceed to update the initial distance matrix D 1 {\displaystyle D_{1}} into a new distance matrix D 2 {\displaystyle D_{2}} (see below), reduced in size by one row and one column because of the clustering of a {\displaystyle a} with b {\displaystyle b} .
Bayesian hierarchical modeling often tries to make an inference on the covariance structure of the data, which can be decomposed into a scale vector and correlation matrix. [3] Instead of the prior on the covariance matrix such as the inverse-Wishart distribution , LKJ distribution can serve as a prior on the correlation matrix along with some ...
An outline, also called a hierarchical outline, is a list arranged to show hierarchical relationships and is a type of tree structure. An outline is used [1] to present the main points (in sentences) or topics of a given subject. Each item in an outline may be divided into additional sub-items.
Ward's minimum variance method is a special case of the objective function approach originally presented by Joe H. Ward, Jr. [1] Ward suggested a general agglomerative hierarchical clustering procedure, where the criterion for choosing the pair of clusters to merge at each step is based on the optimal value of an objective function. This ...
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.