Related papers: Joint Approximate Partial Diagonalization of Large…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using…
Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a $d$-dimensional domain. The application of the inverse operator…
We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition…
An Orthogonally resolvable Matching Design OMD$(n, k)$ is a partition of the edges the complete graph $K_n$ into matchings of size $k$, called blocks, such that the blocks can be resolved in two different ways. Such a design can be…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
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…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair $\{A,L\}$, where we propose three approaches to compute approximate generalized singular…
In this paper, we examine the problem of approximating a general linear dimensionality reduction (LDR) operator, represented as a matrix $A \in \mathbb{R}^{m \times n}$ with $m < n$, by a partial circulant matrix with rows related by…
In this paper we study higher-order difference equations which can be written as follows: $$ \mathbf{J} (y_0,y_1,...)^T = \lambda^N (y_0,y_1,...)^T, $$ where $\mathbf{J}$ is a $(2N+1)$-diagonal bounded banded matrix…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
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…
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an $l_1$ minimization problem…
A matrix framework is presented for the solution of ODEs, including initial-, boundary and inner-value problems. The framework enables the solution of the ODEs for arbitrary nodes. There are four key issues involved in the formulation of…
We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming…