Related papers: A sparse approximate inverse for triangular matric…
We introduce innovative algorithms for computing exact or approximate (minimum-norm) solutions to $Ax=b$ or the {\it normal equation} $A^TAx=A^Tb$, where $A$ is an $m \times n$ real matrix of arbitrary rank. We present more efficient…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's iteration regains its local quadratic convergence toward…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by…
We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering…
We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…
The nonlinear (preconditioned) conjugate gradient N(P)CG method and the locally optimal (preconditioned) minimal residual LO(P)MR method, both of which are used for the iterative computation of sparse approximate inverses (SPAIs) of…
Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…
In this paper, several modifications are introduced to the functional approximation method iterLap to reduce the approximation error, including stopping rule adjustment, proposal of new residual function, starting point selection for…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
In this paper we consider the problem of exact recovery of a fixed sparse vector with the measurement matrices sequentially arriving along with corresponding measurements. We propose an extension of the iterative hard thresholding (IHT)…
In this paper, we provide explicit formulas for the exact inverses of the symmetric tridiagonal near-Toeplitz matrices characterized by weak diagonal dominance in the Toeplitz part. Furthermore, these findings extend to scenarios where the…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
This paper studies sparse nonlinear least squares problems, where the Jacobian matrices are unavailable or expensive to compute, yet have some underlying sparse structures. We construct the Jacobian models by the $ \ell_1 $ minimization…
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…
In this paper we show how to recover a spectral approximations to broad classes of structured matrices using only a polylogarithmic number of adaptive linear measurements to either the matrix or its inverse. Leveraging this result we obtain…