INTLAB is a Matlab toolbox supporting real and complex interval scalars, vectors, and matrices, as well as sparse real and complex interval matrices. It is designed to be very fast. In fact, it isâ€¦ (More)

Algorithms for summation and dot product of floating point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computedâ€¦ (More)

In this paper we describe verification methods for dense and large sparse systems of linear and nonlinear equations. Most of the methods described have been developed by the author. Other methods areâ€¦ (More)

The classical mathematical proof is performed by pencil and paper. However, there are many ways in which computers may be used in a mathematical proof. But "proofs by computers" or even the use ofâ€¦ (More)

In this paper we study the condition number of linear systems, the condition number of matrix inversion, and the distance to the nearest singular matrix, all problems with respect to normwiseâ€¦ (More)

Given a vector of floating-point numbers with exact sum s, we present an algorithm for calculating a faithful rounding of s, i.e. the result is one of the immediate floating-point neighbors of s. Ifâ€¦ (More)

In this paper bounds for clusters of eigenvalues of non-selfadjoint matrices are investigated. We describe a method for the computation of rigorous error bounds for multiple or nearly multipleâ€¦ (More)

Given a vector of floating-point numbers with exact sum s, we present an algorithm for calculating a faithful rounding of s into the set of floating-point numbers, i.e. one of the immediateâ€¦ (More)

It is well known that it is an ill-posed problem to decide whether a function has a multiple root. Even for a univariate polynomial an arbitrary small perturbation of a polynomial coefficient mayâ€¦ (More)