Flexible Conjugate Gradients

Lanczos and Linear Systems Lanczos and Linear Systems

abstract Lanczos's major contributions to the numerical solution of linear equations are contained in two papers: \An Iteration Method for the Solution of the Eigenvalue Problem of Linear Diierential and Integral Operators" and \Solutions of Linear Equations by Minimized Iterations ," the second of which contains the method of conjugate gradients. In this note we retrace Lanczos's journey from ...

Natural Gradients in Practice: Non-Conjugate Variational Inference in Gaussian Process Models

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 with hyperparameter learning. We conclude that the natural gradient can significantly improve performance in terms of wall-clock time. For illconditioned pos...

Parallel Hybrid Sparse Solvers Through Flexible Incomplete Cholesky Preconditioning

We consider parallel preconditioning schemes to accelerate the convergence of Conjugate Gradients (CG) for sparse linear system solution. We develop methods for constructing and applying preconditioners on multiprocessors using incomplete factorizations with selective inversion for improved latency-tolerance. We provide empirical results on the efficiency, scalability and quality of our precond...

Conjugate gradient neural network in prediction of clay behavior and parameters sensitivities

The use of artificial neural networks has increased in many areas of engineering. In particular, this method has been applied to many geotechnical engineering problems and demonstrated some degree of success. A review of the literature reveals that it has been used successfully in modeling soil behavior, site characterization, earth retaining structures, settlement of structures, slope stabilit...

S aled Conjugate Gradients for Maximum Likelihood :