The aim of this paper is to find an accurate and efficient algorithm for evaluating the summation of large sets of floating-point numbers. We present a new representation of the floating-point number system in which a number is represented as a linear combination of integers and the coefficients are powers of the base of the floating-point system. The approach allows to build up an accurate flo...

Given a set P of n points in R, we consider two related problems. Firstly, we study the problem of computing two isothetic unit squares which may be either disjoint or intersecting (having empty common zone) such that they together cover maximum number of points. The time and space complexities of the proposed algorithm for this problem are both O(n). We also study the problem of computing k di...

In 1954 Zelinsky [16] proved that every element in the ring of linear transformations of a vector space V over a division ring D is a sum of two units unless dim V = 1 and D = Z2. Because EndD(V ) is a (von-Neumann) regular ring, Zelinsky’s result generated quite a bit of interest in regular rings that have the property that every element is a sum of (two) units. Clearly, a ring R, having Z2 as...