Computing on sequences of embedded intervals (Q1371154)

A concept for containing computational results with prescribed accuracy is presented. The concept is based on a generalized number representation where the base for the representation is not fixed but can be changed during the expansion of the number. Further, the representation is related to interval sequences, which allow the control of the accuracy of the computation. The steps of the computation are performed with a number of digits as low as possible. This number varies automatically. If the prescribed accuracy has finally not been achieved, a backtracking process is initiated which goes through previous arithmetic operations and decides which of them should be refined. It is demonstrated at the computation of ill-conditioned \(6\times 6\) determinants that the developed concept might work well.