相关论文: On Novel Fixed-Point-Type Iterations with Structur…

We focus on the problem of optimal control of large-scale systems whose models are obtained by discretization of partial differential equations using the Finite Element (FE) or Finite Difference (FD) methods. The motivation for studying…

In this paper, we focus on using optimization methods to solve matrix equations by transforming the problem of solving the Sylvester matrix equation or continuous algebraic Riccati equation into an optimization problem. Initially, we use a…

This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…

We study the Allen-Cahn equation with a cubic-quintic nonlinear term and a stochastic $Q$-trace-class stochastic forcing in two spatial dimensions. This stochastic partial differential equation (SPDE) is used as a test case to understand,…

We revisit and extend the Riccati theory, unifying continuous-time linear-quadratic optimal permanent and sampled-data control problems, in finite and infinite time horizons. In a nutshell, we prove that:-- when the time horizon T tends to…

In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize the FPE in space and time using two well-known numerical…

Continuous-time algebraic Riccati equations can be found in many disciplines in different forms. In the case of small-scale dense coefficient matrices, stabilizing solutions can be computed to all possible formulations of the Riccati…

We present structure preserving integrators for solving linear quadratic optimal control problems. This problem requires the numerical integration of matrix Riccati differential equations whose exact solution is a symmetric positive…

Motivated by Pryce's structural index reduction method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm and propose a fixed-point iteration method with parameters. It leads to a…

In this paper we derive a Toeplitz-structured closed form of the unique positive semi-definite stabilizing solution for the discrete-time algebraic Riccati equations, especially for the case that the state matrix is not stable. Based on the…

Fixed-point iteration algorithms like RTA (response time analysis) and QPA (quick processor-demand analysis) are arguably the most popular ways of solving schedulability problems for preemptive uniprocessor FP (fixed-priority) and EDF…

In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-type methods is developed by integrating the core concept of…

Floating-point arithmetic (FPA) is a mechanical representation of real arithmetic (RA), where each operation is replaced with a rounded counterpart. Various numerical properties can be verified by using SMT solvers that support the logic of…

Stochastic algebraic Riccati equations, also known as rational algebraic Riccati equations, arising in linear-quadratic optimal control for stochastic linear time-invariant systems, were considered to be not easy to solve. The-state-of-art…

This paper describes a systematic approach towards building a new family of neural networks based on a delay-loop version of a reservoir neural network. The resulting architecture, called Scaled-Time-Attention Robust Edge (STARE) network,…

Continuous search problems (CSPs), which involve finding solutions within a continuous domain, frequently arise in fields such as optimization, physics, and engineering. Unlike discrete search problems, CSPs require navigating an…

We develop a new randomized iterative algorithm---stochastic dual ascent (SDA)---for finding the projection of a given vector onto the solution space of a linear system. The method is dual in nature: with the dual being a non-strongly…

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

The discrete dipole approximation (DDA) is a widely used and versatile numerical method for solving electromagnetic scattering by arbitrarily shaped objects. Despite its popularity, quantitative comparisons between independent…

Markov-modulated fluid queues are popular stochastic processes frequently used for modelling real-life applications. An important performance measure to evaluate in these applications is their steady-state behaviour, which is determined by…