Related papers: Localized inverse factorization
This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
In solving a linear system with iterative methods, one is usually confronted with the dilemma of having to choose between cheap, inefficient iterates over sparse search directions (e.g., coordinate descent), or expensive iterates in…
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…
When a matrix has a banded inverse there is a remarkable formula that quickly computes that inverse, using only local information in the original matrix. This local inverse formula holds more generally, for matrices with sparsity patterns…
The inverse-free extreme learning machine (ELM) algorithm proposed in [4] was based on an inverse-free algorithm to compute the regularized pseudo-inverse, which was deduced from an inverse-free recursive algorithm to update the inverse of…
As electronic structure simulations continue to grow in size, the system-size scaling of computational costs increases in importance relative to cost prefactors. Presently, linear-scaling costs for three-dimensional systems are only…
If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…
The algorithms in the current sequential numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multicore architectures. A new family of algorithms, the tile algorithms, has recently been introduced. Previous research…
Iterative majorize-minimize (MM) (also called optimization transfer) algorithms solve challenging numerical optimization problems by solving a series of "easier" optimization problems that are constructed to guarantee monotonic descent of…
We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…
We investigate the problem of factorizing a matrix into several sparse matrices and propose an algorithm for this under randomness and sparsity assumptions. This problem can be viewed as a simplification of the deep learning problem where…
Polynomial factorization over $ZZ$ is of great historical and practical importance. Currently, the standard technique is to factor the polynomial over finite fields first and then to lift to integers. Factorization over finite fields can be…
LU-factorization of matrices is one of the fundamental algorithms of linear algebra. The widespread use of supercomputers with distributed memory requires a review of traditional algorithms, which were based on the common memory of a…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…
This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distinguishes two input regimes. In the right-only regime, where only…
In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…