Titlebook: Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications; Cetraro, Italy 2015 Michele Benzi,Dario Bini,Charles Van L

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0075-8434 ng field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives..978-3-319-49886-7978-3-319-49887-4Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Structured Matrix Problems from Tensors, low-rank manipulations are central to the theme. Algorithmic details include the exploitation of partial symmetries, componentwise optimization, and how we might beat the “curse of dimensionality.” Order-4 tensors figure heavily in the discussion.

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Matrix Structures in Queuing Models,al world. They translate, in matrix language, the specific properties of the physical problem. Often, structured matrices reveal themselves in a clear form and apparently seem to show immediately all their properties. Very often, structures are hidden, difficult to discover, and their properties see

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Matrices with Hierarchical Low-Rank Structures,olution 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 introduction to these techniques, with an emphasis on li

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Localization in Matrix Computations: Theory and Applications, is vanishingly small compared the total number of entries as the size of the system tends to infinity. In other words, the nonnegligible entries tend to be ., or concentrated, around a small region within the computational domain, with rapid decay away from this region (uniformly as the system size

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Groups and Symmetries in Numerical Linear Algebra, translations in the plane and rotations of a sphere. The topic of these lecture notes is applications of group theory in computational mathematics. We will first cover fundamental properties of groups and continue with an extensive discussion of commutative (abelian) groups and their relationship t

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https://doi.org/10.1007/978-1-4842-8939-6s generalisation of Fourier analysis to non-commutative groups and discuss problems in linear algebra with non-commutative symmetries. The representation theory of non-commutative finite groups is used as a tool to efficiently solve linear algebra problems with symmetries, exemplified by the computation of matrix exponentials.

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