Related papers: Bisection-based asymmetric MT2 computation: a high…
Implementations of two algorithms for the transverse Mercator projection are described; these achieve accuracies close to machine precision. One is based on the exact equations of Thompson and Lee and the other uses an extension of…
Matrix code allows one to discover algorithms and to render them in code that is both compilable and is correct by construction. In this way the difficulty of verifying existing code is avoided. The method is especially important for…
A maximum priority matching is a matching in an undirected graph that maximizes a priority score defined with respect to given vertex priorities. An earlier paper showed how to find maximum priority matchings in unweighted graphs. This…
We present an algorithm for computation of cell adjacencies for well-based cylindrical algebraic decomposition. Cell adjacency information can be used to compute topological operations e.g. closure, boundary, connected components, and…
Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum…
Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fi t a model to data without relying on the computation of the model likelihood. They instead require to…
Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
Blurring mean shift (BMS) algorithm, a variant of the mean shift algorithm, is a kernel-based iterative method for data clustering, where data points are clustered according to their convergent points via iterative blurring. In this paper,…
This paper presents a fast algorithm for projecting a given function to the set of shift orthogonal functions (i.e. set containing functions with unit $L^2$ norm that are orthogonal to their prescribed shifts). The algorithm can be…
Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
This paper describes novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run-time needed to find an exact maximum distance of two points in E2. The proposed algorithm has been evaluated…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
For a continuous function $f$ defined on a closed and bounded domain, there is at least one maximum and one minimum. First, we introduce some preliminaries which are necessary through the paper. We then present an algorithm, which is…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…