Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method
Youcef Saad · SIAM Journal on Scientific and Statistical Computing · 1985
This paper presents some practical ways of using polynomial preconditions for solving large sparse linear systems of equations issued from discretizations of partial differential equations. For a symmetric positive definite matrix A these techniques are based on least squares polynomials on the interval $[0,b]$ where b is the Gershgorin estimate of the largest eigenvalue. Therefore, as opposed to previous work in the field, there is no need for computing eigenvalues of A. We formulate a version of the conjugate gradient algorithm that is more suitable for parallel architectures and discuss the advantages of polynomial preconditioning in the context of these architectures.