This paper proposes a probabilistic framework for algorithms that iteratively solve unconstrained linear problems Bx = b with positive definite B for x. The goal is to replace the point estimates returned by existing methods with a Gaussian posterior belief over the elements of the inverse of B, which can be used to estimate errors. Recent probabilistic interpretations of the secant family of q...

Lippert, T., K. Schilling and N. Petkov, Quark propagator on the Connection Machine, Parallel Computing 18 (1992) 1291-1299. The computation of the fermion propagator in lattice Quantum Chromodynamics requires the solution of a large system of linear equations. We discuss and compare the structure, implementation and performance of two linear equation solvers, the Jacobi algorithm and the Conju...

Fluid simulation has been an active research field in computer graphics for the last 30 years. Stam’s stable fluids method, among others, is used for solving equations that govern fluids. This method solves a sparse linear system during the diffusion and move steps, using either relaxation methods (Jacobi, Gauss-Seidel, etc), Conjugate Gradient (and its variants), or others (not subject of stud...

The conjugate gradient methods are outstanding by choosing a suitable for coefficient conjugate. In this paper, modified version of the algorithm suggested Hideaki and Yasushi [4] is proposed in order to show that new method globally convergent, under standard assumptions. To exemplify efficiency method, its performance examined impulse noise removal images.

BACKGROUND Protection against Haemophilus influenzae type b (Hib), a rapidly invading encapsulated bacteria, is dependent on maintenance of an adequate level of serum antibody through early childhood. In many countries, Hib vaccine booster doses have been implemented after infant immunization to sustain immunity. We investigated the long-term persistence of antibody and immunological memory in ...

Model based iterative reconstruction (MBIR) algorithms have been used in clinical studies to allow significant dose reduction in CT scans while maintaining the diagnostic image quality. Simultaneous-update algorithms, which can take advantage of massively parallel computer architectures, are promising to significantly improve the speed of MBIR. To achieve this goal, we also need to improve the ...

In this paper we derive two second-order algorithms, based on conjugate gradient, for on-line training of recurrent neural networks. These azgorithms use two different techniques to extract second-order information on the Hessian matrix without calculating or storing it and without making numericaz approximations. Several simulation results for non-linear system identzjication tests by locally’...

1. Introduction. We consider the resolution of large-scale nonlinear problems arising from the finite-element discretization of geometrically non-linear structural analysis problems. We use a classical Newton Raphson algorithm to handle the non-linearity which leads to the resolution of a sequence of linear systems with non-invariant matrices and right hand sides. The linear systems are solved ...

The trust region step problem, by solving a sphere constrained quadratic programming, plays a critical role in the trust region Newton method. In this paper, we propose an efficient Multi-Stage Conjugate Gradient (MSCG) algorithm to compute the trust region step in a multi-stage manner. Specifically, when the iterative solution is in the interior of the sphere, we perform the conjugate gradient...

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 non-conjugate terms. On the other hand, stochastic-gradient methods can handle the nonconjugate terms but they usually ignore the conjugate structure of the mo...