Verified solution of large systems and global optimization problems

Recent results on the solution of large, banded or sparse systems and on global unconstrained optimization problems including verification of the correctness of the result will be discussed. The computing time for the verification for large linear systems is the same as for the decomposition, the total computational effort for verifying the global optimum value is for well-known test examples competitive to those of pure floating point algorithms. Computational examples will be demonstrated.