Stable Parallel Algorithms for Two-Point Boundary Value Problems

@article{Wright1992StablePA,
  title={Stable Parallel Algorithms for Two-Point Boundary Value Problems},
  author={Stephen J. Wright},
  journal={SIAM J. Scientific Computing},
  year={1992},
  volume={13},
  pages={742-764}
}
Some of the most widely used algorithmsfor two-point boundaryvalue ODEs, namely nite diierence and collocation methods and standard multiple shooting, proceed by setting up and solving a structured system of linear equations. It is well known that the linear system can be set up eeciently in parallel; we show here that a structured orthogonal factorization technique can be used to solve this system, and hence the overall problem, in an eecient, parallel, and stable way. 

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Bounds for rounding errors in the Gaussian elimination for band systems

  • Z. Bohte
  • Journal of the Institute of Mathematics and its…
  • 1975
Highly Influential
8 Excerpts

Parallel solution of special large block tridiagonal systems: Tpbvp

  • M. Lentini
  • 1989
Highly Influential
7 Excerpts

Alternate row and column elimination for solving certain linear systems

  • J. M. Varah
  • SIAM Journal on Numerical Analysis, 13
  • 1976
Highly Influential
7 Excerpts

The Algebraic Eigenvalue Problem

  • J. H. Wilkinson
  • Oxford University Press, London
  • 1965
Highly Influential
6 Excerpts

General framework

  • U. M. Ascher, R.M.M. Mattheij
  • stability and error analysis for numerical sti…
  • 1988
Highly Influential
10 Excerpts

The close relationships between methods for solving two-point boundary value problems

  • M. Lentini, M. R. Osborne, R. D. Russell
  • SIAM Journal on Numerical Analysis, 22
  • 1985
Highly Influential
5 Excerpts

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