Gaussian elimination

@inproceedings{Higham2011GaussianE,
  title={Gaussian elimination},
  author={N. Higham},
  year={2011}
}
As the standard method for solving systems of linear equations, Gaussian elimination GE is one of the most important and ubiquitous numerical algorithms. [...] Key Method Pivoting strategies for ensuring numerical stability are described. Special properties of GE for certain classes of structured matrices are summarized. How to implement GE in a way that efficiently exploits the hierarchical memories of modern computers is discussed.Expand
38 Citations
Alan Turing and the origins of modern Gaussian elimination ∗
  • 1
  • PDF
Alan Turing y los orígenes de la eliminación gaussiana moderna
  • 1
A Flexible CUDA LU-Based Solver for Small, Batched Linear Systems
  • 1
Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations
  • 10
  • PDF
Reducing Memory Requirements for High-Performance and Numerically Stable Gaussian Elimination
  • 2
  • PDF
$AB$-algorithm and its application for solving matrix square roots
  • Highly Influenced
  • PDF
...
1
2
3
4
...

References

SHOWING 1-10 OF 52 REFERENCES
Mathematicians of Gaussian Elimination
  • 51
  • PDF
Recursion leads to automatic variable blocking for dense linear-algebra algorithms
  • F. Gustavson
  • Mathematics, Computer Science
  • IBM J. Res. Dev.
  • 1997
  • 249
Communication Avoiding Gaussian elimination
  • L. Grigori, J. Demmel, Hua Xiang
  • Computer Science
  • 2008 SC - International Conference for High Performance Computing, Networking, Storage and Analysis
  • 2008
  • 31
  • PDF
Accuracy and stability of numerical algorithms
  • 2,649
  • PDF
Error Analysis of Direct Methods of Matrix Inversion
  • 379
Error bounds from extra-precise iterative refinement
  • 101
  • PDF
The growth factor of a Hadamard matrix of order 16 is 16
  • 13
  • PDF
...
1
2
3
4
5
...