Abstract
Let A be an n-by-n nearly singular matrix with Rank(A)≥n - 1 and singular values d1≥⋯≥dn-1 > dn, where dn can be small or zero. Consider the rank-1 modification of A: A ̂=A+αzwT, with {norm of matrix}z{norm of matrix} = {norm of matrix}w{norm of matrix} = 1. We give lower and upper bounds for the condition number of  in terms of |α| and the angles between z and w and the singular vectors of A corresponding to dn.
Original language | English (US) |
---|---|
Pages (from-to) | 223-232 |
Number of pages | 10 |
Journal | Linear Algebra and Its Applications |
Volume | 76 |
Issue number | C |
DOIs | |
State | Published - Apr 1986 |
Externally published | Yes |
Bibliographical note
Funding Information:*The authors were supported in part by the Department of Energy under contract DE-AC02.81ER10996, by the Army Research Office under contract DAAG83-0177, and by a BID-CONICET fellowship from Argentina.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Numerical Analysis
- Algebra and Number Theory