Related papers: Computing with B-series
The role of the descriptor system representation as basis for reliable numerical computations for system analysis and synthesis, and in particular, for the manipulation of rational matrices, is discussed and available robust numerical…
In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…
This paper introduces a novel toolbox named BIDEAL for the generation of biclusters, their analysis, visualization, and validation. The objective is to facilitate researchers to use forefront biclustering algorithms embedded on a single…
Butcher series are combinatorial devices used in the study of numerical methods for differential equations evolving on vector spaces. More precisely, they are formal series developments of differential operators indexed over rooted trees,…
The Libra Toolkit is a collection of algorithms for learning and inference with discrete probabilistic models, including Bayesian networks, Markov networks, dependency networks, and sum-product networks. Compared to other toolkits, Libra…
Basic computer arithmetic operations, such as $+$, $\times$, or $\div$ are correctly rounded, whilst mathematical functions such as $e^x$, $\ln(x)$, or $\sin(x)$ in general are not, meaning that separate implementations may provide…
In this work, we illustrate and explore the use of Taylor series as solutions of differential equations. For a large a number of classes of differential equations in the literature, there are plenty of sources where the well known Taylor…
We introduce a Macaulay2 package for working with jet schemes. The main method constructs jets of ideals, polynomial rings and their quotients, ring homomorphisms, affine varieties, and (hyper)graphs. The package also includes additional…
Differentiating through constrained optimization problems is increasingly central to learning, control, and large-scale decision-making systems, yet practical integration remains challenging due to solver specialization and interface…
We introduce CBXPy and ConsensusBasedX.jl, Python and Julia implementations of consensus-based interacting particle systems (CBX), which generalise consensus-based optimization methods (CBO) for global, derivative-free optimisation. The…
In this article, we introduce the adapted inverse iteration method to generate bicomplex Julia sets associated to the polynomial map $w^2+c$. The result is based on a full characterization of bicomplex Julia sets as the boundary of a…
In this article, we present a recently released R package for Bayesian calibration. Many industrial fields are facing unfeasible or costly field experiments. These experiments are replaced with numerical/computer experiments which are…
We discuss computer implementation of the known algorithm of finding separation coordinates for the special class of orthogonal separable systems called L-systems or Benenti systems.
The INLA package provides a tool for computationally efficient Bayesian modeling and inference for various widely used models, more formally the class of latent Gaussian models. It is a non-sampling based framework which provides…
The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version…
We introduce Gradus.jl, an open-source and publicly available general relativistic ray-tracing toolkit for spectral modelling in arbitrary spacetimes. Our software is written in the Julia programming language, making use of forward-mode…
As astronomical data grows in volume and complexity, the scalability of analysis software becomes increasingly important. At the same time, astrophysics analysis software relies heavily on open-source contributions, so languages and tools…
We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for practical computation in…
Sunny is a Julia package designed to serve the needs of the quantum magnetism community. It supports the specification of a very broad class of spin models and a diverse suite of numerical solvers. These include powerful methods for…
The dirichletprocess package provides software for creating flexible Dirichlet process objects. Users can perform nonparametric Bayesian analysis using Dirichlet processes without the need to program their own inference algorithms. Instead,…