Related papers: Approximating Matrices with Multiple Symmetries
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…
Accurate prediction of molecular correlation energies from first principles requires resolving the {O}(N^4) electron repulsion integral (ERI) tensor. Existing graph neural network approaches to the electronic structure problem often…
In this paper, we assess the performance of adaptive and nested factorized sparse approximate inverses as smoothers in multilevel V-cycles, when smoothing is performed following the Chebyshev iteration of the fourth kind. For our test…
Fixman's work in 1974 and the follow-up studies have developed a method that can factorize the inverse of mass matrix into an arithmetic combination of three sparse matrices---one of them is positive definite and need to be further…
The Cholesky QR algorithm is an efficient communication-minimizing algorithm for computing the QR factorization of a tall-skinny matrix. Unfortunately it has the inherent numerical instability and breakdown when the matrix is…
Matrices with off-diagonal decay appear in a variety of fields in mathematics and in numerous applications, such as signal processing, statistics, communications engineering, condensed matter physics, and quantum chemistry. Numerical…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
The description of weakly bound electronic states is especially difficult with atomic orbital basis sets. The diffuse atomic basis functions that are necessary to describe the extended electronic state generate significant linear…
We present two novel, explicit representations of Cholesky factor of a nonsingular correlation matrix. The first representation uses semi-partial correlation coefficients as its entries. The second, uses an equivalent form of the square…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
A new generalized cyclic symmetric structure in the factor matrices of polyadic decompositions of matrix multiplication tensors for non-square matrix multiplication is proposed to reduce the number of variables in the optimization problem…
We classify a family of matrices of shift operators that can be factorised in a computationally tractable manner with the Cholesky algorithm. Such matrices arise in the linear quadratic regulator problem, and related areas. We use the…
First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also…
We show that Laplacian and symmetric diagonally dominant (SDD) matrices can be well approximated by linear-sized sparse Cholesky factorizations. We show that these matrices have constant-factor approximations of the form $L L^{T}$, where…
Tensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, i.e., symmetric or non-symmetric, invertible…
Given a matrix A \in R^{m x n}, we present a randomized algorithm that sparsifies A by retaining some of its elements by sampling them according to a distribution that depends on both the square and the absolute value of the entries. We…
We present a fast direct algorithm for computing symmetric factorizations, i.e. $A = WW^T$, of symmetric positive-definite hierarchical matrices with weak-admissibility conditions. The computational cost for the symmetric factorization…
Randomly pivoted Cholesky (RPCholesky) is an algorithm for constructing a low-rank approximation of a positive-semidefinite matrix using a small number of columns. This paper develops an accelerated version of RPCholesky that employs block…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
Tensors play a pivotal role in the realms of science and engineering, particularly in the realms of data analysis, machine learning, and computational mathematics. The process of unfolding a tensor into matrices, commonly known as tensor…