Parallel Newton–Chebyshev polynomial preconditioners for the conjugate gradient method. Issue 6 (10th March 2021)

• Record Type: Journal Article
• Authors: Bergamaschi, Luca; Martinez Calomardo, Angeles
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 6(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-03-10
• Subjects: conjugate gradient method -- parallel computing -- polynomial preconditioner -- scalability; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1153
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: In this note, we exploit polynomial preconditioners for the conjugate gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix equation X −1 = A and the Chebyshev polynomials for preconditioning. We propose a simple modification of one parameter which avoids clustering of extremal eigenvalues in order to speed‐up convergence. We provide results on very large matrices (up to 8.6 billion unknowns) in a parallel environment showing the efficiency of the proposed class of preconditioners.