Related papers: Towards 1ULP evaluation of Daubechies Wavelets
Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
The 2-D discrete wavelet transform (DWT) can be found in the heart of many image-processing algorithms. Until recently, several studies have compared the performance of such transform on various shared-memory parallel architectures,…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
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…
Advanced MAVKA software for the approximation of extrema observations is used to analyze the variability of the brightness of pulsating and eclipsing stars, but may be useful in analyzing signals of any nature. A new algorithm using a…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…
A blend of two Taylor series for the same smooth real- or complex-valued function of a single variable can be useful for approximation. We use an explicit formula for a two-point Hermite interpolational polynomial to construct such blends.…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…
The Delta-variance analysis, has proven to be an efficient and accurate method of characterising the power spectrum of interstellar turbulence. The implementation presently in use, however, has several shortcomings. We propose and test an…
A brief sketch of computer methods of involutivity analysis of differential equations is presented in context of its application to study degenerate Lagrangian systems. We exemplify the approach by a detailed consideration of a…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex solution. We analyze various probability…
We propose and study the framework of dissipative statistical solutions for the incompressible Euler equations. Statistical solutions are time-parameterized probability measures on the space of square-integrable functions, whose…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…