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The Leja method is a polynomial interpolation procedure that can be used to compute matrix functions. In particular, computing the action of the matrix exponential on a given vector is a typical application. This quantity is required, e.g.,…
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This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
Julia is a mature general-purpose programming language, with a large ecosystem of libraries and more than 12000 third-party packages, which specifically targets scientific computing. As a language, Julia is as dynamic, interactive, and…
We present a MATLAB package called the Pha-sorArray Toolbox that has been developed to make harmonic analysis and control methods both practical and user-friendly. The toolbox adopts an object-oriented architecture that enables intuitive…
We present a data-assisted iterative regularization method for solving ill-posed inverse problems. The proposed approach, termed \texttt{IRMGL+\(\Psi\)}, integrates classical iterative techniques with a data-driven regularization term…
A multi-prism lens (MPL) is a refractive x-ray lens with one-dimensional focusing properties. If used as a pre-object collimator in a scanning system for medical x-ray imaging, it reduces the divergence of the radiation and improves on…
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Image restoration aims to recover high quality images from inputs degraded by various factors, such as adverse weather, blur, or low light. While recent studies have shown remarkable progress across individual or unified restoration tasks,…
We present the Julia package SagbiHomotopy.jl for solving systems of polynomial equations using numerical homotopy continuation. The package introduces an optimal choice of a start system based on SAGBI homotopies. For square horizontally…
Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
We present the software design of Gridap, a novel finite element library written exclusively in the Julia programming language, which is being used by several research groups world-wide to simulate complex physical phenomena such as…
The Yau-Yau nonlinear filter has increasingly emerged as a powerful tool to study stochastic complex systems. To leverage it to a wider spectrum of application scenarios, we pack the Yau-Yau filtering ALgorithms (YauYauAL) into a package of…
This work presents a guide for the use of some of the functions of the R package "multiColl" for the detection of near multicollinearity. The main contribution, in comparison to other existing packages in R or other econometric software, is…
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining…
This work provides simple algorithms for multi-class (and multi-label) prediction in settings where both the number of examples n and the data dimension d are relatively large. These robust and parameter free algorithms are essentially…
This work presents a guide for the use of some of the functions of the multiColl package in R for the detection of near-multicollinearity. The main contribution, in comparison to other existing packages in R or other econometric software,…