• Corpus ID: 118518503

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}
}
  • A. Bradley
  • Published 12 October 2011
  • Computer Science
  • arXiv: Numerical Analysis
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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13 Citations
Methods Citations
6

13 Citations

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References

SHOWING 1-8 OF 8 REFERENCES

Adaptive Low-Rank Approximation of Collocation Matrices

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

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

Hierarchical Matrices - A Means to Efficiently Solve Elliptic Boundary Value Problems

  • M. Bebendorf
  • Computer Science, Mathematics
    Lecture 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

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

  • Y. Okada
  • Geology
    Bulletin 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)

Adaptive Variable-Rank Approximation of General Dense Matrices

  • S. Börm
  • Computer Science
    SIAM 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.