CHINESE JOURNAL OF COMPUTATIONAL PHYSICS ›› 1992, Vol. 9 ›› Issue (4): 445-447.

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NUMERICAL COMPUTATON FOR EXTREME EIGENVALES OF THE PCG ITERATIVE MATRIX

Ru Xiangyang, Lei Guangyao   

  1. Institute of Applied Mathematics, Academia Sinica, Beijing 100080
  • Received:1992-02-24 Online:1992-12-25 Published:1992-12-25

Abstract: This paper discusses the relationship between the iterative matrix AM-1 of the preconditioned conjugate gradient (PCG) and the tridiagonal matrix Bs obtained when the PCG iteration terminates. The distribution of eigenvalues of Bs is analysed and, consequently, several properties of eigenvalues of the PCG iterative matrix AM-1 are revealed.

Key words: preconditioned conjugate gradient, tridiagonal matrix, eigenvalue extreme eigenva