Algorithm 987. MANBIS -- a C++ mathematical software package for locating and computing efficiently many roots of a function: theoretical issues. MANBIS is a C++ mathematical software package for tackling the problem of computing the roots of a function when the number of roots is very large (of the order of hundreds or thousands). This problem has attracted increasing attention in recent years because of the broad variety of applications in various fields of science and technology. MANBIS applies the bisection method to obtain an approximate root according to a predetermined accuracy. Thus, the only computable information required is the algebraic signs of the considered function, which is the smallest amount of information (one bit of information) necessary for the purpose needed, and not any additional information. MANBIS is able to compute very efficiently a user-given percentage of roots and draws its strength from the fact that the roots are expected to be many. Furthermore, MANBIS is capable of estimating without any additional function computational cost the total number of roots within the user-given interval. Our approach can also be efficiently applied in cases where the distribution of the roots is not known. This article is accompanied by another article where the user manual, some implementation details, and some examples are included.

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