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The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization…
We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of…
Generalized eigenvalue problems (GEPs) find applications in various fields of science and engineering. For example, principal component analysis, Fisher's discriminant analysis, and canonical correlation analysis are specific instances of…
In this paper we present an extremely general method for approximately solving a large family of convex programs where the solution can be divided between different agents, subject to joint differential privacy. This class includes…
We study the problem of privately estimating the parameters of $d$-dimensional Gaussian Mixture Models (GMMs) with $k$ components. For this, we develop a technique to reduce the problem to its non-private counterpart. This allows us to…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
This paper presents a finite element method that preserves (at the degrees of freedom) the eigenvalue range of the solution of tensor-valued time-dependent convection--diffusion equations. Starting from a high-order spatial baseline…
Multi-modal data-sets are ubiquitous in modern applications, and multi-modal Variational Autoencoders are a popular family of models that aim to learn a joint representation of the different modalities. However, existing approaches suffer…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
We describe algorithms for computing eigenpairs (eigenvalue--eigenvector) of a complex $n\times n$ matrix $A$. These algorithms are numerically stable, strongly accurate, and theoretically efficient (i.e., polynomial-time). We do not…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
Several domains increasingly rely on machine learning in their applications. The resulting heavy dependence on data has led to the emergence of various laws and regulations around data ethics and privacy and growing awareness of the need…
We consider the approximation of eigenvalue problems for elasticity equations with interface. This kind of problems can be efficiently discretized by using immersed finite element method (IFEM) based on Crouzeix-Raviart P1-nonconforming…
In this paper we combine an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM). The resulting algorithm (IP-PMM) is interpreted as a primal-dual regularized IPM, suitable for solving linearly constrained…
Given only a collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to solve elliptic partial differential equations (PDEs) supplemented with boundary conditions. Notice…
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant…
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue…
In this paper, a new type of multi-level correction scheme is proposed for solving eigenvalue problems by finite element method. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which…
Recent years have demonstrated that using random feature maps can significantly decrease the training and testing times of kernel-based algorithms without significantly lowering their accuracy. Regrettably, because random features are…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…