A modification to the half-interval search (binary search) method

Abstract

This modification to the half-interval search (binary search) method finds the best computer zero within a fixed number of iterations of the half-interval search algorithm.The paper outlines the modification for use with a computer where floating-point numbers are stored in a fixed length field of thirty-two bits. Also, the floating-point numbers are represented using a hexidecimal base and twenty-four bits to store the fraction.The modification has to do with initially starting with a and b within consecutive powers of sixteen. That is, there exists an integer n such that16n ≤ a < b ≤ 16n+1 or -16n+1 ≤ a < b ≤ -16n. This determines the characteristic of x0. Then a binary search for the fraction of x0 can be completed within twenty-four iterations. If a computer zero of the function is not found in the search, then the a and b of the last iteration are consecutive computer numbers with f(a) and f(b) having opposite signs.