Related papers: Iterated Gauss-Seidel GMRES
We present a general scheme for the construction of new eficient generalized Schultz iterative methods for computing the inverse matrix. These methods have the form $$ X_{k+1} = X_k(a_0^{(k)}I+a_1^{(k)}AX_k),\quad k\in\mathbb{N}, $$ where…
For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…
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…
Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…
In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply…
In this paper, two efficient iterative algorithms based on the simpler GMRES method are proposed for solving shifted linear systems. To make full use of the shifted structure, the proposed algorithms utilizing the deflated restarting…
The rigorous stability analysis of high-order implicit-explicit multistep (IEMS) methods for nonlinear parabolic equations by using discrete energy arguments is a long standing open issue due to their non-A-stable property. A novel…
Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…
We present a new method for the numerical solution of singular integral equations on the real axis. The method's value stems from an explicit formula for the Cauchy integral of a complex exponential multiplied by a rational function.…
Minimal problems in computer vision raise the demand of generating efficient automatic solvers for polynomial equation systems. Given a polynomial system repeated with different coefficient instances, the traditional Gr\"obner basis or…
Unmatched pairs of forward and back projectors are common in X-ray CT computations for large-scale problems; they are caused by the need for fast algorithms that best utilize the computer hardware, and it is an interesting and challenging…
This paper generalizes the proportionate-type adaptive algorithm to the graph signal processing and proposes two proportionate-type adaptive graph signal recovery algorithms. The gain matrix of the proportionate algorithm leads to faster…
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…
Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES)…
Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…
Models of gravitational waveforms play a critical role in detecting and characterizing the gravitational waves (GWs) from compact binary coalescences. Waveforms from numerical relativity (NR), while highly accurate, are too computationally…
Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods…
Randomized iterative algorithms for solving a factorized linear system, $\mathbf A\mathbf B\mathbf x=\mathbf b$ with $\mathbf A\in{\mathbb{R}}^{m\times \ell}$, $\mathbf B\in{\mathbb{R}}^{\ell\times n}$, and $\mathbf b\in{\mathbb{R}}^m$,…