\(\mathcal H^2\)-matrix arithmetics in linear complexity
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Publication:818851
DOI10.1007/s00607-005-0146-yzbMath1086.65036OpenAlexW2069045162MaRDI QIDQ818851
Publication date: 21 March 2006
Published in: Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00607-005-0146-y
algorithmsnumerical experimentspreconditionersfactorizationslinear complexitymatrix operationsformatted matrix operationsHierarchical matrices\(\mathcal H^2\)-matrices
Numerical computation of matrix norms, conditioning, scaling (65F35) Complexity and performance of numerical algorithms (65Y20) Direct numerical methods for linear systems and matrix inversion (65F05)
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Cites Work
- Unnamed Item
- Adaptive recompression of \(\mathcal H\)-matrices for BEM
- Approximation of integral operators by \(\mathcal H^2\)-matrices with adaptive bases
- Rapid solution of integral equations of classical potential theory
- On the fast matrix multiplication in the boundary element method by panel clustering
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
- Construction and arithmetics of \(\mathcal H\)-matrices
- Introduction to hierarchical matrices with applications.
- Variable order panel clustering
- Approximation of integral operators by variable-order interpolation
- Data-sparse approximation by adaptive \({\mathcal H}^2\)-matrices
- \(\mathcal H^2\)-matrix approximation of integral operators by interpolation
- Hybrid cross approximation of integral operators
- Hierarchische Matrizen
- Multiscale Bases for the Sparse Representation of Boundary Integral Operators on Complex Geometry
- Wavelets on Manifolds I: Construction and Domain Decomposition
- A fast algorithm for particle simulations
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