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In this paper, we investigate numerical solutions for inverse singular value problems (for short, ISVPs) arising in various applications. Inspired by the methodologies employed for inverse eigenvalue problems, we propose a Cayley-free…
In this paper we present an algebraic study concerning the general second order linear differential equation with polynomial coefficients. By means of Kovacic's algorithm and asymptotic iteration method we find a degree independent…
Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be…
The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An…
Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review…
A new algorithm for computing coefficients of the Baker--Campbell--Hausdorff series is presented, which can be straightforwardly implemented in any general-purpose programming language or computer algebra system. The algorithm avoids…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
This paper describes the algorithms, features and implementation of PyDEC, a Python library for computations related to the discretization of exterior calculus. PyDEC facilitates inquiry into both physical problems on manifolds as well as…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets. Originally introduced by Collins in the 1970s for use in quantifier elimination it has since found numerous applications within…
We present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
We discuss the great importance of using mathematical software in solving problems in today's society. In particular, we show how to use Mathematica software to solve ordinary differential equations exactly and numerically. We also show how…
There exists a huge number of numerical methods that iteratively construct approximations to the solution $y(x)$ of an ordinary differential equation (ODE) $y'(x)=f(x,y)$ starting from an initial value $y_0=y(x_0)$ and using a finite…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We study quantum algorithms based on quantum (sub)gradient estimation using noisy function evaluation oracles, and demonstrate the first dimension-independent query complexities (up to poly-logarithmic factors) for zeroth-order convex…
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
Context. Many algorithms to solve Kepler's equations require the evaluation of trigonometric or root functions. Aims. We present an algorithm to compute the eccentric anomaly and even its cosine and sine terms without usage of other…
Automatic differentiation is everywhere, but there exists only minimal documentation of how it works in complex arithmetic beyond stating "derivatives in $\mathbb{C}^d$" $\cong$ "derivatives in $\mathbb{R}^{2d}$" and, at best, shallow…
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…