Related papers: Algorithm with variable coefficients for computing…
A few iterations of alternating least squares with a random starting point provably suffice to produce nearly optimal spectral- and Frobenius-norm accuracies of low-rank approximations to a matrix; iterating to convergence is unnecessary.…
Convergence problems in coupled-cluster iterations are discussed, and a new iteration scheme is proposed. Whereas the Jacobi method inverts only the diagonal part of the large matrix of equation coefficients, we invert a matrix which also…
We propose a method for the construction of preconditioners of parameter-dependent matrices for the solution of large systems of parameter-dependent equations. The proposed method is an interpolation of the matrix inverse based on a…
This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
In this paper, based on an optimization problem, a sketch-and-project method for solving the linear matrix equation AXB = C is proposed. We provide a thorough convergence analysis for the new method and derive a lower bound on the…
Construction on the measurement matrix $A$ is a central problem in compressed sensing. Although using random matrices is proven optimal and successful in both theory and applications. A deterministic construction on the measurement matrix…
The dynamic matrix inverse problem is to maintain the inverse of a matrix undergoing element and column updates. It is the main subroutine behind the best algorithms for many dynamic problems whose complexity is not yet well-understood,…
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…
We present a recursive algorithm for multi-coefficient inversion in nonlinear Helmholtz equations with polynomial-type nonlinearities, utilizing the linearized Dirichlet-to-Neumann map as measurement data. To achieve effective recursive…
In this paper, two new efficient algorithms for calculating the sign function of the large-scale sparse matrix are proposed by combining filtering algorithm with Newton method and Newton Schultz method respectively. Through the theoretical…
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues and eigenvectors. In this article we propose a new method for…
The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part…
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
Solutions to differential equations, which are used to model physical systems, are computed numerically by solving a set of discretized equations. This set of discretized equations is reduced to a large linear system, whose solution is…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
In various areas of applied numerics, the problem of calculating the logarithm of a matrix A emerges. Since series expansions of the logarithm usually do not converge well for matrices far away from the identity, the standard numerical…
We extend the geometrical inverse approximation approach for solving linear least-squares problems. For that we focus on the minimization of $1-\cos(X(A^TA),I)$, where $A$ is a given rectangular coefficient matrix and $X$ is the approximate…
This article discusses a more general and numerically stable Rybicki Press algorithm, which enables inverting and computing determinants of covariance matrices, whose elements are sums of exponentials. The algorithm is true in exact…
This paper presents a new algorithm for generating random inverse-Wishart matrices that directly generates the Cholesky factor of the matrix without computing the factorization. Whenever parameterized in terms of a precision matrix…