Related papers: Randomized algorithms for Generalized Hermitian Ei…

Optimization over the set of matrices $X$ that satisfy $X^\top B X = I_p$, referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA),…

Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…

MaxCut is a canonical NP-hard combinatorial optimization problem in graph theory with broad applications ranging from physics to bioinformatics. Although variational quantum algorithms offer promising new approaches that may eventually…

Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem…

Nowadays hybrid evolutionary algorithms, i.e, heuristic search algorithms combining several mutation operators some of which are meant to implement stochastically a well known technique designed for the specific problem in question while…

We propose a new partial decoding algorithm for $h$-interleaved one-point Hermitian codes that can decode-under certain assumptions-an error of relative weight up to $1-(\tfrac{k+g}{n})^{\frac{h}{h+1}}$, where $k$ is the dimension, $n$ the…

We study the generalized eigenvalue problem in $\mathbb{R}^N$ for a general convex nonlinear elliptic operator which is locally elliptic and positively $1$-homogeneous. Generalizing article of Berestycki and Rossi in [Comm. Pure Appl. Math.…

We establish a Karhunen-Lo`eve expansion for generic centered, second order stochastic processes, which does not rely on topological assumptions. We further investigate in which norms the expansion converges and derive exact average rates…

We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA),…

Randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a…

In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…

Detection of abrupt spatial changes in physical properties representing unique geometric features such as buried objects, cavities, and fractures is an important problem in geophysics and many engineering disciplines. In this context,…

In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem, and prove some convergence results for these algorithms and their…

We develop a generalized hybrid iterative approach for computing solutions to large-scale Bayesian inverse problems. We consider a hybrid algorithm based on the generalized Golub-Kahan bidiagonalization for computing Tikhonov regularized…

We introduce a new algorithm for finding the eigenvalues and eigenvectors of Hermitian matrices within a specified region, based upon the LANSO algorithm of Parlett and Scott. It uses selective reorthogonalization to avoid the duplication…

We propose a novel algorithmic framework of Variable Metric Over-Relaxed Hybrid Proximal Extra-gradient (VMOR-HPE) method with a global convergence guarantee for the maximal monotone operator inclusion problem. Its iteration complexities…

We analyze the systematic errors made when using the generalized eigenvalue problem to extract energies and matrix elements in lattice gauge theory. Effective theories such as HQET are also discussed. Numerical results are shown for the…

We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form $T(\lambda)v=0$ that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are…

Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…

In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces for GFEMs based on local eigenvalue problems involving a…