NUMERICAL CALCULATION OF THE INDEX OF A FUNCTION

摘要

The paper gives a new numerical method for calculation of the index of a function: given a function F(x) and F_1(x) = F(X)/|F(x)| : [a,b] → C, a continuous, piecewise linear function F_2(x) is constructed that coincides with F_1(x) at some partition points x_k of the interval [a,b]. If the diameter of the partition renders the variation of F_1(x) in the intervals [x_k,x_(k+1)] (k = 1,n) less than 2, then the index of F(x) is calculated using the intersection points of the graph of F_2(x) with the coordinate axis by a special finite algorithm.