Proceedings Article10.1109/IPDPS.2004.1303284
A parallel QR factorization algorithm for solving Toeplitz tridiagonal systems
R. E. Shaw,L.E. Garey,A.M. White +2 more
- 26 Apr 2004
- pp 235-241
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TL;DR: This work presents two parallel QR factorization algorithms used to solve Toeplitz tridiagonal systems that exhibit high scalability and near linear to superlinear speedup on large system sizes when implemented on a distributed system.
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Abstract: Summary form only given. QR methods for solving Toeplitz tridiagonal systems are well developed with applications in numerous interdisciplinary fields. There is a strong motivation to develop faster, more efficient and, more importantly, scalable algorithms to factor such systems due to their significance in many scientific applications. We present two parallel QR factorization algorithms used to solve Toeplitz tridiagonal systems. QR factorization is accomplished using Householder reflections and Givens rotations. These parallel algorithms exhibit high scalability and near linear to superlinear speedup on large system sizes when implemented on a distributed system.
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Citations
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•Journal Article
Algorithms for Special Tridiagonal Systems.
TL;DR: In this paper, the authors considered the problem of solving symmetric diagonally dominant tridiagonal systems of linear equations with constant diagonals using the Fourier method and the cyclic reduction method of Hockney and Evans.
1
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Wen-Ming Yan,Kuo-Liang Chung +1 more
TL;DR: A fast algorithm for solving the special tridiagonal system, a symmetric diagonally dominant and Toeplitz system of linear equations, which is quite competitive with the Gaussian elimination, cyclic reduction, specialLU factorization, reversed triangular factorizations, and ToEplitz factorization methods.
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Peter Arbenz,Markus Hegland +1 more
- 01 Jan 1996
TL;DR: A stable algorithm for the parallel solution of banded and periodically banded linear systems is proposed that incorporates pivoting without sacri cing e ciency and is based on a bidiagonal cyclic reduction that admits pivoting.
A parallel method for linear equations with tridiagonal Toeplitz coefficient matrices
L.E. Garey,R. E. Shaw +1 more
TL;DR: Nonsymmetric Toepliz systems and nonsymmetric circulant systems are examined and the coefficient matrix is split into two bidiagonal matrices and the efficient solution of the resulting systems is considered.
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