Related papers: Using $LDL^{T}$ factorizations in Newton's method …
We propose a new class of short matrix recurrences for the solution of nonsymmetric linear equations of the type $\mathbf{A}_1\mathbf{X}\mathbf{B}_1+\ldots+\mathbf{A}_p\mathbf{X}\mathbf{B}_p=CD^T$. These iterative methods combine local…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
Newton systems in quadratic programming (QP) methods are often solved using direct Cholesky or LDL factorizations. When the linear systems in successive iterations differ by a low-rank modification (as is common in active set and augmented…
We study the time-inconsistent linear quadratic optimal control problem for forward-backward stochastic differential equations with potentially indefinite cost weighting matrices for both the state and the control variables. Our research…
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
Most linear algebra kernels in interior point methods for linear programming require the solution of linear systems of equation with the matrix $N = A^TD^{-1}A$ (or $AD^{-1}A^T$), where $A$ denotes the constraint matrix of the linear…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
Discrete algebraic Riccati equations and their fixed points are well understood and arise in a variety of applications, however, the time-varying equations have not yet been fully explored in the literature. In this article we provide a…
This paper addresses the stabilization of dynamical systems in the infinite horizon optimal control setting using nonlinear feedback control based on State-Dependent Riccati Equations (SDREs). While effective, the practical implementation…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
Oscillatory second order linear ordinary differential equations arise in many scientific calculations. Because the running times of standard solvers increase linearly with frequency when they are applied to such problems, a variety of…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
This paper proposes a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a study on the generalised discrete algebraic Riccati equation. In…
Sharp large deviation estimates for stochastic differential equations with small noise, based on minimizing the Freidlin-Wentzell action functional under appropriate boundary conditions, can be obtained by integrating certain matrix Riccati…
In this paper we discuss how to decompose the constrained generalized discrete-time algebraic Riccati equation arising in optimal control and optimal filtering problems into two parts corresponding to an additive decomposition X=X0+D of…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
This paper analyzes a special instance of nonsymmetric algebraic matrix Riccati equations arising from transport theory. Traditional approaches for finding the minimal nonnegative solution of the matrix Riccati equations are based on the…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
We consider the problem of computing tractable approximations of time-dependent d x d large positive semi-definite (PSD) matrices defined as solutions of a matrix differential equation. We propose to use "low-rank plus diagonal" PSD…
The efficient numerical integration of large-scale matrix differential equations is a topical problem in numerical analysis and of great importance in many applications. Standard numerical methods applied to such problems require an unduly…