相关论文: On numerical stability of recursive present value …

A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit…

This paper presents a wp-style calculus for obtaining expectations on the outcomes of (mutually) recursive probabilistic programs. We provide several proof rules to derive one-- and two--sided bounds for such expectations, and show the…

In this paper, we consider a novel auxiliary variable method to obtain energy stable schemes for gradient flows. The auxiliary variable based on energy bounded above does not limited to the hypothetical conditions adopted in previous…

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

In this paper, we explore the stability of an inverted pendulum under a generalized parametric excitation described by a superposition of $N$ cosines with different amplitudes and frequencies, based on a simple stability condition that does…

We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this…

Polynomial based methods have recently been used in several works for mitigating the effect of stragglers (slow or failed nodes) in distributed matrix computations. For a system with $n$ worker nodes where $s$ can be stragglers, these…

Mixture models have received considerable attention recently and Newton [Sankhy\={a} Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for estimating a mixing distribution. We prove almost sure consistency of this recursive…

Value Iteration is a widely used algorithm for solving Markov Decision Processes (MDPs). While previous studies have extensively analyzed its convergence properties, they primarily focus on convergence with respect to the infinity norm. In…

Using existing, forward-in-time integration schemes, we demonstrate that it is possible to compute unstable, saddle-type fixed points of stiff systems of ODEs when the stable compenents are fast (i.e., rapidly damped) while the unstable…

Algorithmic recourse provides individuals who receive undesirable outcomes from machine learning systems with minimum-cost improvements to achieve a desirable outcome. However, machine learning models often get updated, so the recourse may…

The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such…

Modern power systems face a grand challenge in grid management due to increased electricity demand, imminent disturbances, and uncertainties associated with renewable generation, which can compromise grid security. The security assessment…

We present rigorous error estimates towards a first-order unconditionally energy stable scheme designed for 3D hydrodynamic Q-tensor model of nematic liquid crystals. This scheme combines the scalar auxiliary variable (SAV), stabilization…

Convergence rates are established for an inexact accelerated alternating direction method of multipliers (I-ADMM) for general separable convex optimization with a linear constraint. Both ergodic and non-ergodic iterates are analyzed.…

The Evans function has been used extensively to study spectral stability of travelling-wave solutions in spatially extended partial differential equations. To compute Evans functions numerically, several shooting methods have been…

Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…

In this work, we propose an a pointwise a posteriori error estimator for conforming finite element approximations of eigenfunctions corresponding to multiple and clustered eigenvalues of elliptic operators. It is proven that the pointwise a…

We show that by using higher order precision arithmetic, i.e., using floating point types with more significant bits than standard double precision numbers, one may accurately compute eigenvalues for non-normal matrices arising in…

Online learning algorithms continually update their models as data arrive, making it essential to accurately estimate the expected loss at the current time step. The prequential method is an effective estimation approach which can be…