相关论文: An Efficient Algorithm For Simulating Fracture Usi…

We consider the least-squares approximation of a matrix C in the set of doubly stochastic matrices with the same sparsity pattern as C. Our approach is based on applying the well-known Alternating Direction Method of Multipliers (ADMM) to a…

Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…

A novel adaptive Markov chain Monte Carlo algorithm is presented. The algorithm utilizes sparsity in the partial correlation structure of a density to efficiently estimate the covariance matrix through the Cholesky factor of the precision…

We address the problem of efficient sparse fixed-rank (S-FR) matrix decomposition, i.e., splitting a corrupted matrix $M$ into an uncorrupted matrix $L$ of rank $r$ and a sparse matrix of outliers $S$. Fixed-rank constraints are usually…

This paper focuses on exploring the sparsity of the inverse covariance matrix $\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky…

We present AMPS, an augmented matrix approach to update the solution to a linear system of equations when the matrix is modified by a few elements within a principal submatrix. This problem arises in the dynamic security analysis of a power…

Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…

A method for quasistatic cohesive fracture is introduced that uses an alternating direction method of multipliers (ADMM) to implement an energy approach to cohesive fracture. The ADMM algorithm minimizes a non-smooth, non-convex potential…

Systematic overview of Newton-Schulz and Durand iterations with convergence analysis and factorizations is presented in the chronological sequence in unified framework. Practical recommendations for the choice of the order and…

Materials with network-like microstructure, including polymers, are the backbone for many natural and human-made materials such as gels, biological tissues, metamaterials, and rubbers. Fracture processes in these networked materials are…

As a prevalent distributed learning paradigm, Federated Learning (FL) trains a global model on a massive amount of devices with infrequent communication. This paper investigates a class of composite optimization and statistical recovery…

We investigate the computation of stable fracture paths in brittle thin films using one-dimensional damage models with an elastic foundation. The underlying variational formulation is non-convex, making the evolution path sensitive to…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky…

In this paper, we develop and test a fast numerical algorithm, called MDI-LR, for efficient implementation of quasi-Monte Carlo lattice rules for computing $d$-dimensional integrals of a given function. It is based on the idea of converting…

Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…

We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…

Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…

We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…