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This paper presents a new Matlab toolbox, aimed at facilitating the use of polynomial optimization for stability analysis of nonlinear systems. In the past decade several decisive contributions made it possible to recast this type of…
A method for evaluating matrix polynomials have recently been developed that require one fewer matrix product ($1M$) than the Paterson--Stockmeyer (PS) method. Since the computational cost for large-scale matrices is asymptotically…
We introduce QCLAB, an object-oriented MATLAB toolbox for constructing, representing, and simulating quantum circuits. Designed with an emphasis on numerical stability, efficiency, and performance, QCLAB provides a reliable platform for…
This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called IR Tools, serves two related purposes: we provide implementations…
We develop an optimization framework for identifying ideal Mixed Binary Linear Programs (MBLP) which is linear when using known input data and nonconvex quadratic over parametric input data. These techniques are applied to various…
PENLAB is an open source software package for nonlinear optimization, linear and nonlinear semidefinite optimization and any combination of these. It is written entirely in MATLAB. PENLAB is a young brother of our code PENNON \cite{pennon}…
Multi-Label Classification toolbox is a MATLAB/OCTAVE library for Multi-Label Classification (MLC). There exists a few Java libraries for MLC, but no MATLAB/OCTAVE library that covers various methods. This toolbox offers an environment for…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
Recently Chen and Gao~\cite{ChenGao2017} proposed a new quantum algorithm for Boolean polynomial system solving, motivated by the cryptanalysis of some post-quantum cryptosystems. The key idea of their approach is to apply a Quantum Linear…
Algorithm portfolio and selection approaches have achieved remarkable improvements over single solvers. However, the implementation of such systems is often highly customised and specific to the problem domain. This makes it difficult for…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
In this paper we present MLaut (Machine Learning AUtomation Toolbox) for the python data science ecosystem. MLaut automates large-scale evaluation and benchmarking of machine learning algorithms on a large number of datasets. MLaut provides…
This paper studies, for the first time, a bilevel polynomial program whose constraints involve uncertain linear constraints and another uncertain linear optimization problem. In the case of box data uncertainty, we present a sum of squares…
A fundamental problem in computational algebraic geometry is the computation of the resultant. A central question is when and how to compute it as the determinant of a matrix. whose elements are the coefficients of the input polynomials…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
Polynomial quantified entailments with existentially and universally quantified variables arise in many problems of verification and program analysis. We present PolyQEnt which is a tool for solving polynomial quantified entailments in…
We present a novel, global algorithm for solving polynomial multiparameter eigenvalue problems (PMEPs) by leveraging a hidden variable tensor Dixon resultant framework. Our method transforms a PMEP into one or more univariate polynomial…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
The `equation-free toolbox' empowers the computer-assisted analysis of complex, multiscale systems. Its aim is to enable you to immediately use microscopic simulators to perform macro-scale system level tasks and analysis, because…
There have been some effective tools for solving (constant/parametric) semi-algebraic systems in Maple's library RegularChains since Maple 13. By using the functions of the library, e.g., RealRootClassfication, one can prove and discover…