Splitting iterations for circulant‐plus‐diagonal systems | Zendy

Ho ManKiu | Zendy; Ng Michael K. | Zendy

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Splitting iterations for circulant‐plus‐diagonal systems

Author(s) -

Ho ManKiu,

Ng Michael K.

Publication year - 2005

Publication title -

numerical linear algebra with applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.02

H-Index - 53

eISSN - 1099-1506

pISSN - 1070-5325

DOI - 10.1002/nla.451

Subject(s) - mathematics , circulant matrix , eigenvalues and eigenvectors , coefficient matrix , diagonal , convergence (economics) , linear system , matrix (chemical analysis) , hermitian matrix , matrix splitting , tridiagonal matrix , mathematical analysis , square matrix , combinatorics , symmetric matrix , pure mathematics , geometry , physics , materials science , quantum mechanics , economics , composite material , economic growth

We consider the system of linear equations ( C + iD ) x = b , where C is a circulant matrix and D is a real diagonal matrix. We study the technique for constructing the normal/skew‐Hermitian splitting for such coefficient matrices. Theoretical results show that if the eigenvalues of C have positive real part, the splitting method converges to the exact solution of the system of linear equations. When the eigenvalues of C have non‐negative real part, the convergence conditions are also given. We present a successive overrelaxation acceleration scheme for the proposed splitting iteration. Numerical examples are given to illustrate the effectiveness of the method. Copyright © 2005 John Wiley & Sons, Ltd.

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