An Introduction to Hierarchical Matrices

An Introduction to Hierarchical Matrices

Matrices with hierarchical low-rank structures

Matrices with low-rank off-diagonal blocks are a versatile tool to perform matrix compression and to speed up various matrix operations, such as the solution of linear systems. Often, the underlying block partitioning is described by a hierarchical partitioning of the row and column indices, thus giving rise to hierarchical low-rank structures. The goal of this chapter is to provide a brief int...

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

Introduction to hierarchical matrices with applications

We give a short introduction to methods for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods, as the inverses of partial differential operators or as solutions of control problems. The result of the approximation will be so-called hierarchical matrices (or short H-matrices). These matrices form a subset of ...

Comparison of Error Tree Analysis and TRIPOD BETA in Accident Analysis of a Power Plant Industry Using Hierarchical Analysis

Introduction: Due to the importance and necessity of accident analysis, it is necessary to use proper technique for precise accident analysis and to provide corrective and preventive measures to prevent recurrence of an accident. Method: In this descriptive-analytical paper, the most important criteria for investigating and selecting accident investigation and analysis techniques and selecting...