相关论文: Instability of the Sherman-Morrison formula and st…

In this paper, we recast the variational formulation corresponding to the single layer boundary integral operator $\operatorname{V}$ for the wave equation as a minimization problem in $L^2(\Sigma)$, where $\Sigma := \partial \Omega \times…

We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are…

Enhancing the stability of machine learning algorithms under distributional shifts is at the heart of the Out-of-Distribution (OOD) Generalization problem. Derived from causal learning, recent works of invariant learning pursue strict…

The Sherman-Woodbury-Morrison (SWM) formula gives an explicit formula for the inverse perturbation of a matrix in terms of the inverse of the original matrix and the perturbation. This formula is useful for numerical applications. We have…

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…

We perform a backward stability analysis of preconditioned sketched GMRES [Nakatsukasa and Tropp, SIAM J. Matrix Anal. Appl, 2024] for solving linear systems $Ax=b$, and show that the backward stability at iteration $i$ depends on the…

We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [T. Blass and L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the…

We derive the precise stability criterion for smooth solitary waves in the b-family of Camassa-Holm equations. The smooth solitary waves exist on the constant background. In the integrable cases b = 2 and b = 3, we show analytically that…

We establish sharp stability results for of non--selfadjoint the ascent and descent spectra under strong resolvent convergence (SRS), a natural framework for finite element approximations of non-selfadjoint and singularly perturbed…

The stability of classical semi-implicit scheme, and some more advanced iterative schemes recently proposed for Numerical Weather Prediction (NWP) purpose is examined. In all these schemes, the solution of the centred-implicit non-linear…

The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…

We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…

In this paper, we study the inverse random source scattering problem for the biharmonic Schrodinger equation in two and three dimensions. The driven source is assumed to be a generalized microlocally isotropic Gaussian random function whose…

We establish a stability result for the Shannon-McMillan-Breiman theorem on the one-sided finite shift space. For any shift-invariant probability measure P and any data-dependent parsing whose number of blocks is sublinear in N almost…

It has been the standard teaching of today that backward stability analysis is taught as absolute, just as in Newtonian physics time is taught absolute time. We will prove it is not true in general. It depends on algorithms. We will prove…

Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…

One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

In this paper, we investigate an inverse random source problem concerned with recovering the strength of a random, uncorrelated acoustic source from correlation measurements of emitted time-harmonic acoustic waves. Such problems arise in…

The article presents a generalization of Sherman-Morrison-Woodbury (SMW) formula for the inversion of a matrix of the form A+sum(U)k)*V(k),k=1..N).