Preconditioned conjugate gradients for solving singular systems

Solving semidefinite programs using preconditioned conjugate gradients

Methods of Conjugate Gradients for Solving Linear Systems

The advent of electronic computers in the middle of the 20th century stimulated a flurry of activity in developing numerical algorithms that could be applied to computational problems much more difficult than those solved in the past. The work described in this paper [1] was done at the Institute for Numerical Analysis, a part of NBS on the campus of UCLA [2]. This institute was an incredibly f...

Methods of Conjugate Gradients for Solving Linear Systems

An iterative algorithm is given for solving a system Ax= k of n linear equations in n unknowns. The solution is given in n steps . It is shown that this method is a special case of a very general met hod which also includes Gaussian elimination . These general algorithms are essentially algorithms for findin g an n dimensional ellipsoid . Connections a re m ade wit h the theory of orthogonal po...

Parallel Preconditioned Conjugate-Gradients Methods on Transputer Networks

We show how highly efficient parallel implementations of basic linear algebra routines may be used as building blocks to implement efficient higher level algorithms. We discuss the solution of systems of linear equations using a preconditioned Conjugate-Gradients iterative method on a network of transputers. Results are presented for the solution of both dense and sparse systems; the latter bei...

A Parallel Preconditioned Conjugate Gradient Package for Solving Sparse Linear Systems on a Cray Y-mp *

In this paper we discuss current activities at Cray Research to develop general-purpose, production-quality software for the eecient solution of sparse linear systems. In particular, we discuss our development of a package of iterative methods that includes Conjugate Gradient and related methods (GMRES, ORTHOMIN and others) along with several preconditioners (incomplete Cholesky and LU factoriz...