A projection strategy for improving the preconditioner in the LOBPCG

• Autorzy: Ma Tailai , Sun Shuli , Zheng Fangyi , Chen Pu

Identyfikatory

DOI

10.61822/amcs-2025-0020

• Języki publikacji: EN

Abstrakty

EN

The computational methods for solving the generalized eigenvalue problems of real symmetric matrices are crucial in fields such as structural dynamics analysis. As the scale of the problems to be solved increases, higher efficiency in solving eigenvalue problems is demanded. The LOBPCG (locally optimal block preconditioned conjugate gradient) method is a promising iterative algorithm suitable for solving large-scale eigenvalue problems, capable of quickly solving multiple extreme eigenpairs. In the LOBPCG, the preconditioner can be executed by calling the truncated PCG to approximately solve the ‘inner’ linear system. However, the convergence rate of the LOBPCG is highly sensitive to the quality of its preconditioner. Only when paired with an appropriate preconditioner, the LOBPCG is notably efficient in minimizing the iterations needed for convergence. This paper proposed a projection strategy which can enhance the quality of the preconditioner, thus improving the overall efficiency and stability of the LOBPCG. The projection strategy first utilizes intermediate vectors from the PCG iterations to construct search subspaces and constraint subspaces for oblique projection, and then executes the oblique projection in truncated PCG when solving inner linear system. This oblique projection technique can find a more accurate approximate solution which minimizes the 2-norm residuals in the search subspace without significantly increasing computational cost, thereby improving the quality of the preconditioner, thus accelerating convergence of the LOBPCG. Numerical experiments show that the projection strategy can improve the LOBPCG algorithm significantly in terms of efficiency and stability.

Słowa kluczowe

EN

LOBPCG; preconditioner; preconditioned conjugate gradient; PCG; projection method

PL

LOBPCG; metoda gradientów sprzężonych; PCG; metoda rzutowania

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2025
• Tom: Vol. 35, no. 2
• Strony: 281--292
• Opis fizyczny: Bibliogr. 30 poz., tab., wykr.

Twórcy

autor

Ma Tailai

• Department of Mechanics and Engineering Science, Peking University, Yiheyuan Road No. 5, 100871 Beijing, China

autor

Sun Shuli

• Department of Mechanics and Engineering Science, Peking University, Yiheyuan Road No. 5, 100871 Beijing, China

autor

Zheng Fangyi

• Intelligent Science & Technology Academy of CASIC, Fucheng Road No. 8, 100830 Beijing, China

autor

Chen Pu

• Department of Mechanics and Engineering Science, Peking University, Yiheyuan Road No. 5, 100871 Beijing, China

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).