Theoretical analysis of the extended cyclic reduction algorithm

The extended cyclic reduction algorithm developed by Swarztrauber in 1974 was used to solve the block-tridiagonal linear system. The paper fills in the gap of theoretical results concerning the zeros of matrix polynomial \(B_{i}^{(r)}\) with respect to a tridiagonal matrix which are computed by Newt...

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Bibliographic Details
Published inarXiv.org
Main Authors Diao, Xuhao, Hu, Jun, Ma, Suna
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.04.2022
Subjects
Algorithms
Critical point
Eigenvalues
Error analysis
Newton methods
Polynomials
Reduction
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Summary:The extended cyclic reduction algorithm developed by Swarztrauber in 1974 was used to solve the block-tridiagonal linear system. The paper fills in the gap of theoretical results concerning the zeros of matrix polynomial \(B_{i}^{(r)}\) with respect to a tridiagonal matrix which are computed by Newton's method in the extended cyclic reduction algorithm. Meanwhile, the forward error analysis of the extended cyclic reduction algorithm for solving the block-tridiagonal system is studied. To achieve the two aims, the critical point is to find out that the zeros of matrix polynomial \(B_{i}^{(r)}\) are eigenvalues of a principal submatrix of the coefficient matrix.
ISSN:2331-8422