Related papers: A robust and efficient implementation of LOBPCG
This paper provides a comprehensive estimation framework for large covariance matrices via a log-det heuristics augmented by a nuclear norm plus $\ell_{1}$-norm penalty. We develop the model framework, which includes high-dimensional…
We present an efficient method for computing dominant eigenvalues of large, nonsymmetric, diagonalizable matrices based on an adaptive block Lanczos algorithm combined with Chebyshev polynomial filtering. The proposed approach improves…
With advances in deep learning, exponential data growth and increasing model complexity, developing efficient optimization methods are attracting much research attention. Several implementations favor the use of Conjugate Gradient (CG) and…
One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales…
We revisit the stochastic limited-memory BFGS (L-BFGS) algorithm. By proposing a new framework for the convergence analysis, we prove improved convergence rates and computational complexities of the stochastic L-BFGS algorithms compared to…
Properties of Superiorized Preconditioned Conjugate Gradient (SupPCG) algorithms in image reconstruction from projections are examined. Least squares (LS) is usually chosen for measuring data-inconsistency in these inverse problems.…
Conjugate gradient is an efficient algorithm for solving large sparse linear systems. It has been utilized to accelerate the computation in Bayesian analysis for many large-scale problems. This article discusses the applications of…
We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…
In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
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…
The sparsity constrained rank-one matrix approximation problem is a difficult mathematical optimization problem which arises in a wide array of useful applications in engineering, machine learning and statistics, and the design of…
We study the high-order local discontinuous Galerkin (LDG) method for the $p$-Laplace equation. We reformulate our spatial discretization as an equivalent convex minimization problem and use a preconditioned gradient descent method as the…
We study the stability of the Lanczos algorithm run on problems whose eigenvector empirical spectral distribution is near to a reference measure with well-behaved orthogonal polynomials. We give a backwards stability result which can be…
Applications in High-Performance Computing (HPC) environments face challenges due to increasing complexity. Among them, the increasing usage of sparse data pushes the limits of data structures and programming models and hampers the…
We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides…
The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems Ax = b, where A is a symmetric positive definite matrix. Rather than computing residuals directly, it updates…
Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal…