A note on level-2 condition numbers (Q558006)

Condition numbers, defined generally as quotients of the relative output error by the relative input error, are discussed. The definition of the condition number is modified to be helpful also for the case of a discrete set of outputs. Such condition numbers can be used for a general class of problems such as feasibility of linear (and more general) programs, the problem of computing an optimal basis of a linear program or a complementary partition problem. When estimating the condition number of any problem the question arises what is the condition number of the condition number which is called the level-2 condition number. Here, previous results on level-2 condition numbers are extended. The results show that level-2 condition numbers differ only slightly from the original ones. This fact is illustrated by 2 examples.