Verification methods or reliable computing aims on producing mathematically
correct answers to numerical problems using solely floating-point arithmetic.
Verification methods produce correct error bounds for the solution of a problem
including the proof of existence and possibly uniqueness or, if the problem is
too ill-conditioned, a corresponding message.
In this talk we will introduce all necessary tools to implement such methods.
As an example we treat systems of nonlinear equations and (constraint) optimization.
Both problems are treated in two ways, locally and globally. In the latter case
error bounds for all roots or for the global minimum within a box are computed.
Computational results are demonstrated in Matlab/Octave.