Related papers: Applications of Conjugate Gradient in Bayesian com…
A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
We would like to congratulate the authors of "A Bayesian Conjugate Gradient Method" on their insightful paper, and welcome this publication which we firmly believe will become a fundamental contribution to the growing field of probabilistic…
This Paper conducts a thorough simulation study to assess the effectiveness of various acceleration techniques designed to enhance the conjugate gradient algorithm, which is used for solving large linear systems to accelerate Bayesian…
The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive definite coefficient matrices. Our CG-based implementation of…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models…
We study the conjugate gradient method for solving s system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
One of the great triumphs in the history of numerical methods was the discovery of the Conjugate Gradient (CG) algorithm. It could solve a symmetric positive-definite system of linear equations of dimension N in exactly N steps. As many…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…
A scaled conjugate gradient method that accelerates existing adaptive methods utilizing stochastic gradients is proposed for solving nonconvex optimization problems with deep neural networks. It is shown theoretically that, whether with…
The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored. We examine how natural gradients can be used in non-conjugate stochastic settings, together…
This paper proposes a generalization of the conjugate gradient (CG) method used to solve the equation $Ax=b$ for a symmetric positive definite matrix $A$ of large size $n$. The generalization consists of permitting the scalar control…
The recent article "A Bayesian conjugate gradient method" by Cockayne, Oates, Ipsen, and Girolami proposes an approximately Bayesian iterative procedure for the solution of a system of linear equations, based on the conjugate gradient…
We revisit the problem of large-scale bundle adjustment and propose a technique called Multidirectional Conjugate Gradients that accelerates the solution of the normal equation by up to 61%. The key idea is that we enlarge the search space…
Variational inference is computationally challenging in models that contain both conjugate and non-conjugate terms. Methods specifically designed for conjugate models, even though computationally efficient, find it difficult to deal with…
Bayesian coresets have emerged as a promising approach for implementing scalable Bayesian inference. The Bayesian coreset problem involves selecting a (weighted) subset of the data samples, such that the posterior inference using the…
A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…