Related papers: Magnus integrators for linear and quasilinear dela…
This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…
The Boris algorithm, a closely related variational integrator and a newly proposed filtered variational integrator are studied when they are used to numerically integrate the equations of motion of a charged particle in a non-uniform strong…
We consider a class of linear Vlasov partial differential equations driven by Wiener noise. Different types of stochastic perturbations are treated: additive noise, multiplicative It\^o and Stratonovich noise, and transport noise. We…
We present a novel deep learning-based algorithm to accelerate - through the use of Artificial Neural Networks (ANNs) - the convergence of Algebraic Multigrid (AMG) methods for the iterative solution of the linear systems of equations…
We present a new method for the numerical solution of singular integral equations on the real axis. The method's value stems from an explicit formula for the Cauchy integral of a complex exponential multiplied by a rational function.…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
For the unitary operator, solution of the Schroedinger equation corresponding to a time-varying Hamiltonian, the relation between the Magnus and the product of exponentials expansions can be expressed in terms of a system of first order…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…
The Magnus expansion offers a method to express a time-ordered exponential as an ordinary operatorial exponential. This representation has advantageous theoretical properties, while still solving the original differential equation. For any…
Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
Differentiable quantum dynamics require automatic differentiation of a complex-valued initial value problem, which numerically integrates a system of ordinary differential equations from a specified initial condition, as well as the…
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…