相关论文: Grassmannian spectral shooting
We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original problem into the problem of computing the unstable manifold at…
We construct and analyze a projection-free linearly implicit method for the approximation of flows of harmonic maps into spheres. The proposed method is unconditionally energy stable and, under a sharp discrete regularity condition,…
Estimation of the properties of a physical system with minimal uncertainty is a central task in quantum metrology. Optical phase estimation is at the center of many metrological tasks where the value of a physical parameter is mapped to the…
Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely…
A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single…
Graph generation is a fundamental task with wide applications in modeling complex systems. Although existing methods align the spectrum or degree profile of the target graph, they often ignore the geometry induced by eigenvectors and the…
This work addresses a central challenge in the numerical analysis of the cutoff spatially homogeneous Boltzmann equation: the development of rigorously justified, accurate numerical schemes. We present (i) a novel Fourier spectral method…
We present a pseudo-spectral method for solving the three-dimensional Boussinesq equations in unbounded cylindrical domains, specifically tailored for rotating, stably stratified flows subject to strong azimuthal shear. To effectively…
We present a method, based on commutator methods, for the spectral analysis of uniquely ergodic dynamical systems. When applicable, it leads to the absolute continuity of the spectrum of the corresponding unitary operators. As an…
The Evans function has become a standard tool in the mathematical study of nonlinear wave stability. In particular, computation of its zero set gives a convenient numerical method for determining the point spectrum of the associated linear…
Coherent Raman scattering spectroscopy is studied purposely, with the Gaussian ultrashort pulses as a hands-on elucidatory extraction tool of the clean coherent Raman resonant spectra from the overall measured data contaminated with the…
Dense flow visualization is a popular visualization paradigm. Traditionally, the various models and methods in this area use a continuous formulation, resting upon the solid foundation of functional analysis. In this work, we examine a…
We examine the spectral stability of travelling waves of the haptotaxis model studied in Harley et al (2014a). In the process we apply Li\'enard coordinates to the linearised stability problem and use a Riccati-transform/Grassmanian…
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analysis. Recently, several works were devoted to the derivation…
State-of-the-art scene flow algorithms pursue the conflicting targets of accuracy, run time, and robustness. With the successful concept of pixel-wise matching and sparse-to-dense interpolation, we push the limits of scene flow estimation.…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
Here we present a numerical method for finding non-hydrostatic coastal-trapped wave and instability solutions to the non-hydrostatic Boussinesq equations in the presence of a background flow and complicated coastal topography. We use…
The processing, storage and transmission of large-scale point clouds is an ongoing challenge in the computer vision community which hinders progress in the application of 3D models to real-world settings, such as autonomous driving, virtual…
In this paper we discuss the stability of an alternative pollution-free procedure for computing spectra. The main difference with the Galerkin method lies in the fact that it gives rise to a weak approximate problem which is quadratic in…
We propose a quasi-Grassmannian gradient flow model for eigenvalue problems of linear operators, aiming to efficiently address many eigenpairs. Our model inherently ensures asymptotic orthogonality: without the need for initial…