We study an average condition number and an average loss of precision for the solution of linear equations and prove that the average case is strongly related to the worst case. This holds if the perturbations of the matrix are measured in Frobenius or spectral norm or componentwise. In particular, for the Frobenius norm we show that one gains about log2n+0.9 bits on the average as compared to the worst case, n being the dimension of the system of linear equations.
|Number of pages||24|
|Journal||Linear Algebra and Its Applications|
|State||Published - Nov 1986|
Bibliographical noteFunding Information:
*This research was supported in part by the National Science Foundation DCR-82-14322 (G. W. W. and H. W.) and Grant MC%3241267 (M. S.).
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics