Related papers: Analytical Solvers for Common Algebraic Equations …
This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…
We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving…
Over the past few years, robotics simulators have largely improved in efficiency and scalability, enabling them to generate years of simulated data in a few hours. Yet, efficiently and accurately computing the simulation derivatives remains…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…
Identifying computational tasks suitable for (future) quantum computers is an active field of research. Here we explore utilizing quantum computers for the purpose of solving differential equations. We consider two approaches: (i) basis…
In this article, we discuss the numerical solution of Boolean polynomial programs by algorithms borrowing from numerical methods for differential equations, namely the Houbolt scheme, the Lie scheme, and a Runge-Kutta scheme. We first…
In this paper, we introduce and study a class of resolvent dynamical systems to investigate some inertial proximal methods for solving mixed variational inequalities. These proposed methods along with their discretizations and derived rates…
We present a novel approach for solving articulated inverse kinematic problems (e.g., character structures) by means of an iterative dual-quaternion and exponentialmapping approach. As dual-quaternions are a break from the norm and offer a…
In this paper we present an efficient computational and symbolic algorithms for solving a backward pentadiagonal linear systems. The implementation of the algorithms using Computer Algebra Systems (CAS) such as MAPLE, MACSYMA, MATHEMATICA,…
A new robust algorithm for the numerical computation of biarcs, i.e. $G^1$ curves composed of two arcs of circle, is presented. Many algorithms exist but are based on geometric constructions, which must consider many geometrical…
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…
In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…
Tensegrity mechanisms have several interesting properties that make them suitable for a number of applications. Their analysis is generally challenging because the static equilibrium conditions often result in complex equations. A class of…
This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…
The general inverse kinematics (IK) problem of a manipulator, namely that of acquiring the self-motion manifold (SMM) of all admissible joint angles for a desired end-effector pose, plays a vital role in robotics modeling, planning and…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We present an algorithm for determining the minimal order differential equations associated to a given Feynman integral in dimensional or analytic regularisation. The algorithm is an extension of the Griffiths-Dwork pole reduction adapted…
We use the methods of group theory to reduce the equations of motion of two spin systems in (2+1) dimensions to sets of coupled ordinary differential equations. We present solutions of some classes of these sets and discuss their physical…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…