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Splitting iterations for circulant-plus-diagonal systems

✍ Scribed by Man-Kiu Ho; Michael K. Ng

Book ID
102547638
Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
134 KB
Volume
12
Category
Article
ISSN
1070-5325

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✦ Synopsis

Abstract

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 Β© 2005 John Wiley & Sons, Ltd.

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A new modification of the Rojo method fo
A new modification of the Rojo method for solving symmetric circulant five-diagonal systems of linear equations
✍ S.M. El-Sayed; I.G. Ivanov; M.G. Petkov πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 369 KB

A new, effective, and stable modification of the Rojo method [1] for solving of real symmetric circulant five-diagonal systems of linear equations is proposed. This special kind of system appears in many applications: spline approximation, difference solution of partial differential equations, etc.