Calculating non-equidistant discretizations generated by Blaschke products

Abstract

The argument functions of Blaschke products provide a very elegant way of handling non-uniformity of discretizations. In this paper we analyse the efficiency of numerical methods as the bisection method and Newton's method in the case of calculating non-equidistant discretizations generated by Blaschke products. By taking advantage of the strictly increasing property of argument functions we may calculate the discrete points in an enhanced order — to be introduced here. The efficiency of the discrete points' sequential calculation in this order is significantly increased compared to the naive implementation. In our research we are primarily motivated by ECG curves which usually have alternating regions of high or low variability, and therefore different degree of discretization is needed at different regions of the signals.