A Sparse H-Matrix Arithmetic. Part II: Application to Multi-Dimensional Problems

By Wolfgang Hackbusch, Boris N. Khoromskij. Computing, 2000

413 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computer Graphics and Computer-Aided Design, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/783c80682575682a02f47507348449ba70df0675

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In Atomic and Molecular Physics, and Optics

In Computer Graphics and Computer-Aided Design

In Electrical and Electronic Engineering

Citations in the corpus

Adaptive Low-Rank Approximation of Collocation Matrices (2003, methodology): “Usually, algorithms as in [8, 1] are used to partition the matrix appropriately.”
Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations (2012, methodology): “These methods include fast multipole (FMM) [63, 38], panel clustering [64, 121], Hmatrices [65, 67], matrix skeletonization [99, 37], and hierarchically semiseparable (HSS) matrices [33, 32, 149, 98].”
Domain-decomposition Based ℌ-LU Preconditioners (2007, methodology): “A standard (or strong) admissibility condition has been employed in most previous papers [7, 9 , 5, 6, 1] and is given by”
Hierarchical matrix techniques for low- and high-frequency Helmholtz problems (2007, methodology): “H-matrix techniques have already been successfully applied to integral equations with asymptotically smooth kernel functions(∙, ∙) (seeBebendorf, 2000; Börm & Grasedyck, 2004; Hackbusch & Khoromskij, 2000).”
Fast algorithms for hierarchically semiseparable matrices (2010, neutral): “…systems [ 1–4 ] , least squares problems [ 5 ] , eigenvalue problems [ 6–11 ] , PDEs [ 12–15 ] , integral equations [ 16–18 ] , etc. Examples of rank-structured matrices include H -matrices [ 19–21 ] , H 2 -matrices [ 22–24 ] , quasiseparable matrices [ 25 ] , and semiseparable matrices [ 26–28 ] .”
A bibliography on semiseparable matrices* (2005, background): “This class is also closely related to the class of semiseparable and sequentially semiseparable matrices (see [19, 72, 73] and the references therein).”
Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling (2008, methodology): “The hierarchical matrix (H-matrix) technique [46, 50, 51 , 55] (see also the mosaic-skeleton method [82]) allows an efficient treatment of dense matrices arising, e.g., from BEM, evaluation of volume integrals and multi-particle interactions, certain matrix-valued functions, etc.”