On the existence and computation of $LU$-factorizations with small pivots

@article{Chan1984OnTE,
  title={On the existence and computation of \$LU\$-factorizations with small pivots},
  author={T. Chan},
  journal={Mathematics of Computation},
  year={1984},
  volume={42},
  pages={535-547}
}
  • T. Chan
  • Published 1984
  • Mathematics
  • Mathematics of Computation
Let A be an n by n matrix which may be singular with a one-dimensional null space, and consider the LU-factorization of A. When A is exactly singular, we show conditions under which a pivoting strategy will produce a zero n th pivot. When A is not singular, we show conditions under which a pivoting strategy will produce an nth pivot that is O(G,,) or O(K(A)), where ,, is the smallest singular value of A and K(A) is the condition number of A. These conditions are expressed in terms of the… Expand
70 Citations

Tables from this paper

The Probability of Large Diagonal Elements in the QR Factorization
  • L. Foster
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
  • 1990
  • 15
Rank revealing QR factorizations
  • 376
Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization
  • 551
  • PDF
On Rank-Revealing Factorisations
  • 126
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 23 REFERENCES
An Improved Algorithm for Computing the Singular Value Decomposition
  • T. Chan
  • Mathematics, Computer Science
  • TOMS
  • 1982
  • 228
  • PDF
Estimating Matrix Condition Numbers
  • 23
  • PDF
The Bordering Algorithm and Path Following Near Singular Points of Higher Nullity
  • 102
  • PDF
On the Implicit Deflation of Nearly Singular Systems of Linear Equations
  • 34
...
1
2
3
...