Related papers: Coupled quasi-harmonic bases
The characteristic polynomials of the adjacency matrix of line graphs of caterpillars and then the characteristic polynomials of their Laplacian or signless Laplacian matrices are characterized, using recursive formulas. Furthermore, the…
We extend a classical approximation result of harmonic functions in planar domains due to Bernstein and Walsch to the setting of harmonic functions in Riemann surfaces. This result gives an exact characterization of the rate at which a…
Boundary conforming coordinates are commonly used in plasma physics to describe the geometry of toroidal domains, for example, in three-dimensional magnetohydrodynamic equilibrium solvers. The magnetohydrodynamic equilibrium configuration…
Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These…
In this paper, we describe a new algorithm that approximates the extreme eigenvalue/eigenvector pairs of a symmetric matrix. The proposed algorithm can be viewed as an extension of the Jacobi eigenvalue method for symmetric matrices…
Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…
Many coupled problems in engineering and science can be described by elliptic partial differential equations on adjacent domains, where the coupling can be considered either as a thin equidimensional overlap between the model domains, or as…
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been…
Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps…
For compact domains with smooth boundaries, we present an approximation scheme for surface spline approximation that delivers precise $L_p$ approximation orders on well known smoothness spaces. This scheme overcomes the boundary effects…
We revisit the problem of spectral clustering in multimodal settings, where each data modality is encoded as a graph Laplacian. While classical approaches--including joint diagonalization, spectral co-regularization, and multiview…
Simultaneous matrix diagonalization is used as a subroutine in many machine learning problems, including blind source separation and paramater estimation in latent variable models. Here, we extend algorithms for performing joint…
Recent developments in deep learning have revolutionized the paradigm of image restoration. However, its applications on real image denoising are still limited, due to its sensitivity to training data and the complex nature of real image…
In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time series have led to state-of-the art…
In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…
We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…
We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…
Correspondence-based shape models are key to various medical imaging applications that rely on a statistical analysis of anatomies. Such shape models are expected to represent consistent anatomical features across the population for…
Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating F, whose components satisfy the same relations.
In this article, we design fast algorithms for the computation of approximant bases in shifted Popov normal form. We first recall the algorithm known as PM-Basis, which will be our second fundamental engine after polynomial matrix…