Related papers: GMRES with Singular Vector Approximations

We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…

The rapid growth of circuit complexity has rendered Model Order Reduction (MOR) a key enabler for the efficient simulation of large circuit models. MOR techniques based on moment-matching are well established due to their simplicity and…

The convergence of the restarted GMRES method can be significantly improved, for some problems, by using a weighted inner product that changes at each restart. How does this weighting affect convergence, and when is it useful? We show that…

This research considers a scalable inference for spatial data modeled through Gaussian intrinsic conditional autoregressive (ICAR) structures. The classical estimation method, restricted maximum likelihood (REML), requires repeated…

A randomized Gram-Schmidt algorithm is developed for orthonormalization of high-dimensional vectors or QR factorization. The proposed process can be less computationally expensive than the classical Gram-Schmidt process while being at least…

Most current prevalent iterative methods can be classified into the so-called extended Krylov subspace methods, a class of iterative methods which do not fall into this category are also proposed in this paper. Comparing with traditional…

Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…

A key consideration in the development of numerical schemes for time-dependent partial differential equations (PDEs) is the ability to preserve certain properties of the continuum solution, such as associated conservation laws or other…

In this work, we develop an alternating nonlinear Generalized Minimum Residual (NGMRES) algorithm with depth $m$ and periodicity $p$, denoted by aNGMRES($m, p$), applied to linear systems. We provide a theoretical analysis to quantify by…

We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems…

In this paper, we develop an efficient spectral-Galerkin-type search extension method (SGSEM) for finding multiple solutions to semilinear elliptic boundary value problems. This method constructs effective initial data for multiple…

In many contexts Gaussian Mixtures (GM) are used to approximate probability distributions, possibly time-varying. In some applications the number of GM components exponentially increases over time, and reduction procedures are required to…

We consider linear parameter-dependent 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…

Reconstructing high-quality images with sharp edges requires the use of edge-preserving constraints in the regularized form of the inverse problem. The use of the $\ell_q$-norm on the gradient of the image is a common such constraint. For…

We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…

This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…

The discretization of convection-diffusion equations by implicit or semi-implicit methods leads to a sequence of linear systems usually solved by iterative linear solvers such as GMRES. Many techniques bearing the name of \emph{recycling…

We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…

In large-scale X-ray computed tomography (CT), matrix-free iterative methods are essential due to the prohibitive cost of explicitly forming the system matrix. In practice, forward projectors and backprojectors are often implemented with…

Sampling from Gaussian Markov random fields (GMRFs), that is multivariate Gaussian ran- dom vectors that are parameterised by the inverse of their covariance matrix, is a fundamental problem in computational statistics. In this paper, we…