Conditionally optimal algorithms and estimation of reduced order models

The paper presents some extensions of the optimality results obtained in previous work on algorithms used in the field of system identification in the light of information-based complexity. In particular, a class of conditional algorithms is defined by means of a restriction on the space of solution elements and a corresponding conditional worst case error is introduced. We define conditional central algorithms and show their optimality. A conditional central algorithm is then constructed by modifying a projection algorithm and obtaining in this way a conditional projection algorithm. This algorithm is shown to enjoy local optimality properties with reference to the problem element space within the class of conditionally correct algorithms. Finally, it is shown how these results can be used to handle the problem of reduced order model estimation.