Related papers: Symmetric matrix inversion using modified Gaussian…
We focus on inverse preconditioners based on minimizing $F(X) = 1-\cos(XA,I)$, where $XA$ is the preconditioned matrix and $A$ is symmetric and positive definite. We present and analyze gradient-type methods to minimize $F(X)$ on a suitable…
In the current paper the authors linked two methods in order to evaluate general n-th order tridiagonal determinants. A breakdown free numerical algorithm is developed for computing the inverse of any nxn general nonsingular tridiagonal…
We propose efficient computational methods to fit multivariate Gaussian additive models, where the mean vector and the covariance matrix are allowed to vary with covariates, in an empirical Bayes framework. To guarantee the…
We explore new approaches for finding matrix multiplication algorithms in the commutative setting by adapting the flip graph technique: a method previously shown to be effective for discovering fast algorithms in the non-commutative case.…
In this paper, we prove that if the matrix of the linear system is symetric, the Cholesky decomposition can be obtained from the Gauss elimination method without pivoting, without proving that the matrix of the system is positive definite.
We give a self-contained randomized algorithm based on shifted inverse iteration which provably computes the eigenvalues of an arbitrary matrix $M\in\mathbb{C}^{n\times n}$ up to backward error $\delta\|M\|$ in…
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines,…
A modification of the generalized shift-splitting (GSS) method is presented for solving singular saddle point problems. In this kind of modification, the diagonal shift matrix is replaced by a block diagonal matrix which is symmetric…
This paper describes a fast and stable algorithm for evaluating Bermudan swaption under the two factor Hull-White model. We discretize the calculation of the expected value in the evaluation of Bermudan swaption by numerical integration,…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…
The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…
We develop sampling methods, which consist of Gaussian invariant versions of random walk Metropolis (RWM), Metropolis adjusted Langevin algorithm (MALA) and second order Hessian or Manifold MALA. Unlike standard RWM and MALA we show that…
We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…
We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
For the nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) parts, the modified generalized shift-splitting (MGSSP) preconditioner as well as the MGSSP iteration method are derived in this paper, which generalize…
We propose a novel approach to computationally efficient GP training based on the observation that square-exponential (SE) covariance matrices contain several off-diagonal entries extremely close to zero. We construct a principled procedure…