Since conjugate gradient method and preconditioner contain mainly matrix-vector and matrix-matrix multiplications, convincing results are obtained in terms of both speed and scalability.
📌 3 Key Takeaways
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Objective & Hypothesis:A parallel implementation for linear set of equations of the form Ax = b is presented in this paper.
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Key Findings & Data:The conjugate gradient method is accelerated with an approximate inverse matrix preconditioner obtained from a linear combination of matrix-valued Chebyshev polynomials.
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Conclusion & Impact:Since conjugate gradient method and preconditioner contain mainly matrix-vector and matrix-matrix multiplications, convincing results are obtained in terms of both speed and scalability.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
A parallel implementation for linear set of equations of the form Ax = b is presented in this paper. In this implementation, instead of the traditional direct solution of Ax = b, conjugate gradient method is used. The conjugate gradient method is accelerated with an approximate inverse matrix preconditioner obtained from a linear combination of matrix-valued Chebyshev polynomials. This implementation is tested on a Sun SMP machine. Since conjugate gradient method and preconditioner contain mainly matrix-vector and matrix-matrix multiplications, convincing results are obtained in terms of both speed and scalability.
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Cite This Article
DAĞ, H., AKÇADOĞAN, Ç. (2022). A parallel implementation of Chebyshev preconditioned conjugate gradient method. ARI The Bulletin of the Istanbul Technical University, Cilt: 53 - Sayı: 2, 13–21. https://ajindex.com/articles/448183