Sparse approximation

About: Sparse approximation is a research topic. Over the lifetime, 18037 publications have been published within this topic receiving 497739 citations. The topic is also known as: Sparse approximation.

Accuracy and convergence properties of the fixed‐stress iterative solution of two‐way coupled poromechanics

Abstract: Summary The paper deals with the numerical solution of Biot's equations of coupled consolidation obtained by a mixed formulation combining continuous Galerkin finite-element and multipoint flux approximation finite-volume methods. The solution algorithm relies on the recently developed fixed-stress solution scheme, in which first the flow problem and then the mechanical one are addressed iteratively. We show that the algorithm can be interpreted as a particular block triangular preconditioning strategy applied within a Richardson iteration. The key component to the success of the preconditioner is the sparse approximation to the Schur complement based on a pressure space mass matrix scaled by a weighting factor that depends element-wise on the inverse of a suitable bulk modulus. The accuracy of the method is assessed, making use of well-known analytical solutions from the literature. Numerical results demonstrate robustness and low computational cost of the fixed-stress scheme in accurately capturing the two-way coupling between deformation and pressure. Copyright © 2015 John Wiley & Sons, Ltd.

Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm

Abstract: Two codes are discussed, COLAMD and SYMAMD, that compute approximate minimum degree orderings for sparse matrices in two contexts: (1) sparse partial pivoting, which requires a sparsity preserving column pre-ordering prior to numerical factorization, and (2) sparse Cholesky factorization, which requires a symmetric permutation of both the rows and columns of the matrix being factorized. These orderings are computed by COLAMD and SYMAMD, respectively. The ordering from COLAMD is also suitable for sparse QR factorization, and the factorization of matrices of the form ATA and AAT, such as those that arise in least-squares problems and interior point methods for linear programming problems. The two routines are available both in MATLAB and C-callable forms. They appear as built-in routines in MATLAB Version 6.0.

A Review of Fast L(1)-Minimization Algorithms for Robust Face Recognition

Abstract: : `1-minimization refers to finding the minimum `1-norm solution to an underdetermined linear system b = Ax. It has recently received much attention, mainly motivated by the new compressive sensing theory that shows that under quite general conditions the minimum `1-norm solution is also the sparsest solution to the system of linear equations. Although the underlying problem is a linear program, conventional algorithms such as interior-point methods suffer from poor scalability for large-scale real world problems. A number of accelerated algorithms have been recently proposed that take advantage of the special structure of the `1-minimization problem. In this paper we provide a comprehensive review of five representative approaches, namely, Gradient Projection, Homotopy, Iterative Shrinkage-Thresholding, Proximal Gradient, and Augmented Lagrange Multiplier. The work is intended to fill in a gap in the existing literature to systematically benchmark the performance of these algorithms using a consistent experimental setting. In particular, the paper will focus on a recently proposed face recognition algorithm, where a sparse representation framework has been used to recover human identities from facial images that may be affected by illumination occlusion, and facial disguise. MATLAB implementations of the algorithms described in this paper have been made publicly available.