The algebraic eigenvalue problem
The algebraic eigenvalue problem
Average-case stability of Gaussian elimination
SIAM Journal on Matrix Analysis and Applications
A collection of problems for which Gaussian elimination with partial pivoting is unstable
SIAM Journal on Scientific Computing
Gaussian Elimination with Partial Pivoting Can Fail in Practice
SIAM Journal on Matrix Analysis and Applications
The growth factor and efficiency of Gaussian elimination with rook pivoting
Journal of Computational and Applied Mathematics - Special issue: dedicated to William B. Gragg on the occasion of his 60th Birthday
Error Analysis of Direct Methods of Matrix Inversion
Journal of the ACM (JACM)
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
On the stability of Gauss-Jordan elimination with pivoting
Communications of the ACM
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Three mysteries of Gaussian elimination
ACM SIGNUM Newsletter
Scaled Pivots and Scaled Partial Pivoting Strategies
SIAM Journal on Numerical Analysis
Growth factors of pivoting strategies associated with Neville elimination
Journal of Computational and Applied Mathematics
A note on matrices with maximal growth factor for Neville elimination
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
Several definitions of growth factors for Gaussian elimination are compared. Some new pivoting strategies, intermediate between partial pivoting and rook pivoting, are introduced. For random matrices, an approximation of the average normalized growth factor associated with several pivoting strategies is computed and analyzed. A stationary behavior of the expected growth factors of the new pivoting strategies is observed. Bounds for the growth factors of these pivoting strategies are provided. It is also shown that partial pivoting by columns produces small growth factors for matrices appearing in practical observations and for which the growth factors produced by partial pivoting are very large.