In many practical situations, e.g., in aerospace applications and in mammography, it is important to test the structural integrity of material structures. We show that interval methods can help.

The interval discrete logarithm problem is defined as follows: Given some g, h in a group G, and some N ∈ N such that gz = h for some z where 0 ≤ z < N , find z. At the moment, kangaroo methods are the best low memory algorithm to solve the interval discrete logarithm problem. The fastest non parallelised kangaroo methods to solve this problem are the three kangaroo method, and the four kangaro...

In this paper, we investigate the possibility of using interval arithmetic for rigorous investigations of periodic orbits in discrete-time dynamical systems with special emphasis on chaotic systems. We show that methods based on interval arithmetic when implemented properly are capable of finding all period-n cycles for considerable large n. We compare several interval methods for finding perio...

that if we place money in the bank that pays this interest and withdraw the amount A every year, we will get exactly 0 after n-th withdrawal. Knowing q enables us to make decisions about whether to invest in this annuity or not: e.g., if this q is smaller than the actual bank's interest rate 90, then it is better to leave the money in the bank; if q is larger than qo, then it is better to inves...

Though the hybrid system model checker HYTECH has successfully verified some systems, it restricts the dynamics to linear hybrid automata. We have designed an algorithm capable of verifying systems with more general dynamics. This algorithm uses interval numerical methods to conservatively overapproximate the reachable states of a hybrid automaton. We have implemented our new algorithm in HYTEC...

This paper compares the performance and efficiency of different function range interval methods for plotting f(x, y) = 0 on a rectangular region based on a subdivision scheme, where f(x, y) is a polynomial. The solution of this problem has many applications in CAGD. The methods considered are interval arithmetic methods (using the power basis, Bernstein basis, Horner form and centred form), aff...

Interval methods for solving problems in differential equations and their implementation in floating-point interval arithmetic are interesting due to interval-solutions obtained which contain not only the errors of methods, but also all possible numerical errors. Such methods have been analyzed in a number of papers and monographs (see e.g. [1], [5], [9], and [10]). In our previous papers expli...

When large datasets are aggregated into smaller data sizes we need more complex data tables e.g. interval type instead of standard ones. Our investigation in this paper aims at extending kernel methods to interval data analysis and using graphical methods to explain the obtained results. No algorithmic changes are required from the usual case of continuous data other than the modification of th...