Linear systems whose coefficients have large uncertainties arise routinely in finite element calculations for structures with
uncertain geometry, material properties, or loads. However, a true worst case analysis of the influence of such uncertainties
was previously possible only for very small systems and uncertainties, or in special cases where the coefficients do not exhibit
dependence.
This paper presents a method for computing rigorous bounds on the solution of such systems, with a computable overestimation
factor that is frequently quite small. The merits of the new approach are demonstrated by computing realistic bounds for some
large, uncertain truss structures, some leading to linear systems with over 5000 variables and over 10000 interval parameters,
with excellent bounds for up to about 10% input uncertainty.
Also discussed are some counterexamples for the performance of traditional approximate methods for worst case uncertainty
analysis.