Related papers: Functions to Support Input and Output of Intervals
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by…
Graded modalities have been proposed in recent work on programming languages as a general framework for refining type systems with intensional properties. In particular, continuous endomaps of the discrete time scale, or time warps, can be…
Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods to find optimal values for these parameters. Solving a quantum computational problem with such…
Robustness problems due to the substitution of the exact computation on real numbers by the rounded floating point arithmetic are often an obstacle to obtain practical implementation of geometric algorithms. If the adoption of the --exact…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…
We show that the coding of rotation by $\alpha$ on $m$ intervals with rationally independent lengths can be recoded over $m$ Sturmian words of angle $\alpha.$ More precisely, for a given $m$ an universal automaton is constructed such that…
This paper proposes round-hashing, which is suitable for data storage on distributed servers and for implementing external-memory tables in which each lookup retrieves at most a single block of external memory, using a stash. For data…
A numerical procedure and its MAPLE implementation capable of rigorously, albeit in a brute-force manner, proving specific strict one-variable inequalities in specific finite intervals is described. The procedure is useful, for instance, to…
We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretisation errors…
Following recent interest in correctly rounded math library functions (as currently recommended by the IEEE 754 standard), we have designed several SIMD algorithms for one-input single precision functions and integrated them into our CPU…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…
The necessity of radix conversion of numeric data is an indispensable component in any complete analysis of digital computation. In this paper, we propose a binary encoding for mixed-radix digits. Second, a variant of rANS coding based on…
Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper we briefly review the binary fixed-point representation in an…
The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
This paper is concerned with the exact solution of mixed-integer programs (MIPs) over the rational numbers, i.e., without any roundoff errors and error tolerances. Here, one computational bottleneck that should be avoided whenever possible…
Rounding linear programs using techniques from discrepancy is a recent approach that has been very successful in certain settings. However this method also has some limitations when compared to approaches such as randomized and iterative…
When releasing binary proportions computed using sensitive data, several government agencies and other data stewards protect confidentiality of the underlying values by ensuring the released statistics satisfy differential privacy.…