Related papers: Backward Stability of Explicit External Deflation …
The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros…
This paper presents a method for extrinsic camera calibration (estimation of camera rotation and translation matrices) from a sequence of images. It is assumed camera intrinsic matrix and distortion coefficients are known and fixed during…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity…
Stellarator optimization is a multi-objective, non-convex problem characterized by a complex objective landscape containing many local minima. The solution resulting from a single optimization is highly sensitive to factors such as the…
We present a method for computing locally varying nonlinear mechanical properties in particle simulations of amorphous solids. Plastic rearrangements outside a probed region are suppressed by introducing an external field that directly…
The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in…
Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for…
Essential matrix averaging, i.e., the task of recovering camera locations and orientations in calibrated, multiview settings, is a first step in global approaches to Euclidean structure from motion. A common approach to essential matrix…
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…
Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…
Let $\om $ be a bounded domain in an $n$-dimensional Euclidean space $\Bbb R^n$. We study eigenvalues of an eigenvalue problem of a system of elliptic equations: $$ \{\aligned &\Delta {\mathbf u}+ \alpha{\rm grad}(\text{div}{\mathbf…
We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix $M\in\mathbb{C}^{n\times n}$ up to backward error $\delta\|M\|$ in…
The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…
The instability of embedding spaces across model retraining cycles presents significant challenges to downstream applications using user or item embeddings derived from recommendation systems as input features. This paper introduces a novel…
We present a general method to obtain the stable lasing solutions for the steady-state ab-initio lasing theory (SALT) for the case of a degenerate symmetric laser in two dimensions (2d). We find that under most regimes (with one…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
By reducing the number of global synchronization bottlenecks per iteration and hiding communication behind useful computational work, pipelined Krylov subspace methods achieve significantly improved parallel scalability on present-day HPC…
In this article, we provide stability estimates for the finite element discretization of a class of inverse parameter problems of the form $-\nabla\cdot(\mu S) = \g f$ in a domain $\Omega$ of $\R^d$. Here $\mu$ is the unknown parameter to…
The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar…