SIAM Journal on Matrix Analysis and Applications

Hottopixx, proposed by Bittorf et al. at NIPS 2012, is an algorithm for solving nonnegative matrix factorization (NMF) problems under the separability assumption. Separable NMFs have important applications, such as topic extraction from documents and ...

We present methods for computing the generalized polar decomposition of a matrix based on the dynamically weighted Halley iteration. This method is well established for computing the standard polar decomposition. A stable implementation is available, ...

Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy intermediate-scale quantum (...

We present the analytical singular value decomposition of the stoichiometry matrix for a spatially discrete reaction-diffusion system. The motivation for this work is to develop a matrix decomposition that can reveal hidden spatial flux patterns of ...

In this work, we consider the Takagi factorization of a matrix valued function depending on parameters. We give smoothness and genericity results and pay particular attention to the concerns caused by having either a singular value equal to 0 or multiple ...

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic ...

We analyze when an arbitrary matrix pencil is strictly equivalent to a dissipative Hamiltonian pencil and show that this heavily restricts the spectral properties. In order to relax the spectral properties, we introduce matrix pencils with coefficients that ...

In this paper we show how to construct diagonal scalings for arbitrary matrix pencils $\lambda B-A$, in which both $A$ and $B$ are complex matrices (square or nonsquare). The goal of such diagonal scalings is to “balance” in some sense the row and column ...

We study the convergence of computed quantities to singular triplets in the serial and parallel block-Jacobi singular value decomposition (SVD) algorithm with dynamic ordering. After eliminating possible zero singular values by two finite decompositions of ...

Quantum subspace diagonalization methods are an exciting new class of algorithms for solving large-scale eigenvalue problems using quantum computers. Unfortunately, these methods require the solution of an ill-conditioned generalized eigenvalue problem, ...

The UTV decompositions are promising and computationally efficient alternatives to the singular value decomposition (SVD), which can provide high-quality information about rank, range, and nullspace. However, for large-scale matrices, we want more ...

Global and block Krylov subspace methods are efficient iterative solvers for large sparse linear systems with multiple right-hand sides. However, global or block Lanczos-type solvers often exhibit large oscillations in the residual norms and may have a ...

Solving evolutionary equations in a parallel-in-time manner is an attractive topic. The iterative algorithm based on the block $\alpha$-circulant preconditioning technique has shown promising advantages, especially for hyperbolic problems. By fast Fourier ...

We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be the case for polynomial matrices expressed in the monomial basis. If the ...

We consider linear parameterized systems $A(\mu) x(\mu) = b$ for many different $\mu$, where $A$ is large and sparse and depends nonlinearly on $\mu$. Solving such systems individually for each $\mu$ would require great computational effort. In this work ...

We show to what extent the accuracy of the inner products computed in the GMRES iterative solver can be reduced as the iterations proceed without affecting the convergence rate or final accuracy achieved by the iterates. We bound the loss of orthogonality in ...

Factorization of regular Hermitian valued trigonometric polynomials (on the unit circle) and Hermitian valued polynomials (on the real line) have been studied well. In this paper we drop the condition of regularity and study factorization of singular ...

We propose new variants of the sketch-and-project method for solving large scale ridge regression problems. First, we propose a new momentum alternative and provide a theorem showing it can speed up the convergence of sketch-and-project, through a fast ...

The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to quantum tomography of impure ...