Author(s)

HaiFeng Liu

Affiliation(s)

School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai 519082, Guangdong, China.

Corresponding Author

HaiFeng Liu

ABSTRACT

During the process of typhoon forecasting, numerious symmetric positive definite linear systems are needed to be solved. They are often solved by conjugate gradient method with preconditioning technique. This paper focuses on the convergence rate analysis of conjugate gradient method. The properties of Chebyshev polynomial and Krylov subspace are utilized. The effect of the right-hand-side vector are considered. Several convergence rate estimations are given. Compared with the existing estimation results, the presented results are more exact. This enable us to construct more efficient preconditioners to forecast typhoon more quickly.

KEYWORDS

Typhoon forecasting; Conjugate gradient method; Convergence rate; Eigenvalue

CITE THIS PAPER

HaiFeng Liu. The convergence rate analysis of conjugate gradient method in typhoon forecasting. Frontiers in Environmental Research. 2024, 2(3): 6-10. DOI: https://doi.org/10.61784/fer3011.

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