Abstract
An approach is surveyed to show that verification of numerical computation can be done by a cost around 2〜4 times than that of usual computation. In this approach the floating point numbers arithmetic with rounding toward ±∞ is utilized. By considering inner products of vectors as units of computation, it is shown that drastic reduction of numbers of changing rounding direction in achieved. Moreover, by this approach programming of verification becomes extremely simple. Taking examples such as the matrix equation, polynomial evaluation, nonlinear equation, it is shown that verified solutions for these problems can be obtained by a cost about 2〜4 times than that of computation of approximate solutions.
