On the performance of parallel approximate inverse preconditioning using Java multithreading techniques

• Published in: Applied mathematics and computation Vol. 190; no. 1; pp. 255 - 270
• Main Authors: Gravvanis, George A., Epitropou, Victor N., Giannoutakis, Konstantinos M.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.07.2007; Elsevier
• Subjects: Algebra; Algebraic geometry; Arrow-type matrix; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Exact sciences and technology; Java multithreading; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical linear algebra; Object oriented methodology; Parallel approximate inverse matrix algorithm; Parallel conjugate gradient type methods; Preconditioning; Sciences and techniques of general use; Symmetric multiprocessor systems; Object oriented methodology; Symmetric multiprocessor systems; Java multithreading; Arrow-type matrix; Parallel conjugate gradient type methods; Parallel approximate inverse matrix algorithm; Preconditioning; Conjugate gradient method; Parallel algorithm; Numerical linear algebra; Implementation; Multiprocessor; Direct method; Numerical analysis; Linear system; System performance; Matrix inversion; Applied mathematics; Symmetric system; Object oriented; Shared memory
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2007.01.024

In this paper a parallel shared memory Java multithreaded design and implementation of the explicit approximate inverse preconditioning is presented for solving efficiently arrow-type linear systems on symmetric multiprocessor systems. A new parallel algorithm for computing a class of optimized approximate inverse matrix is introduced. The performance on a symmetric multiprocessor system, using Java multithreading, is investigated by solving characteristic arrow-type linear systems and numerical results are given, considering the parallel performance of the construction of the optimized approximate inverse and the explicit preconditioned generalized conjugate gradient square scheme.