H-Matrix and Block Error Tolerances
@article{Bradley2011HMatrixAB, title={H-Matrix and Block Error Tolerances}, author={Andrew M. Bradley}, journal={arXiv: Numerical Analysis}, year={2011} }
We describe a new method to map the requested error tolerance on an H-matrix approximation to the block error tolerances. Numerical experiments show that the method produces more efficient approximations than the standard method for kernels having singularity order greater than one, often by factors of 1.5 to 5 and at a lower computational cost.
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References
SHOWING 1-8 OF 8 REFERENCES
Adaptive Low-Rank Approximation of Collocation Matrices
- Computer ScienceComputing
- 2003
The proposed algorithm which uses the ℋ-matrix format is purely algebraic and relies on a small part of the collocation matrix for its blockwise approximation by low-rank matrices.
Hybrid cross approximation of integral operators
- Computer ScienceNumerische Mathematik
- 2005
This article uses the -matrix representation that approximates the dense stiffness matrix in admissible blocks by low-rank matrices by a new hybrid algorithm that has the same proven convergence as standard interpolation but also the same efficiency as the (heuristic) adaptive cross approximation (ACA).
Introduction to Hierarchical Matrices with Applications
- Mathematics, Computer Science
- 2003
Hierarchical Matrices - A Means to Efficiently Solve Elliptic Boundary Value Problems
- Computer Science, MathematicsLecture Notes in Computational Science and Engineering
- 2008
The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients and presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions.
Variable Order Panel Clustering
- Computer ScienceComputing
- 2000
A new version of the panel clustering method for a sparse representation of boundary integral equations is presented, which employs more general block partitionings and a variable order of approximation is used depending on the size of blocks.
Internal deformation due to shear and tensile faults in a half-space
- GeologyBulletin of the Seismological Society of America
- 1992
A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite…
The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering)
- Mathematics
- 2007
Adaptive Variable-Rank Approximation of General Dense Matrices
- Computer ScienceSIAM J. Sci. Comput.
- 2007
This paper introduces an algorithm which can construct variable-rank approximations for general matrices without the need of an in-depth analysis of the underlying operators: the matrix is fed into the algorithm, and the algorithm approximates it up to an arbitrary precision.