ISSN:
1573-1340
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Recently, Ning & Kearfott derived a formula for the interval enclosure of the solution set of linear systems of equations with uncertain data ranging in intervals, in the case when the coefficient matrix is an H-matrix. The enclosure is optimal when the midpoint matrix is diagonal, and when the midpoint is the identity, it reduces to the optimal method for enclosing preconditioned systems found by Hansen and Bliek and simplified by Rohn. An elementary proof of this formula is given using only simple properties of H-matrices and Schur complements. The new proof gives additional insight into why the theorem is true. It is also shown how to preserve rigor in the enclosure when finite precision arithmetic is used.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009997221089
