Conjugate gradient algorithms using multiple recursions
Conference
·
OSTI ID:440695
Much is already known about when a conjugate gradient method can be implemented with short recursions for the direction vectors. The work done in 1984 by Faber and Manteuffel gave necessary and sufficient conditions on the iteration matrix A, in order for a conjugate gradient method to be implemented with a single recursion of a certain form. However, this form does not take into account all possible recursions. This became evident when Jagels and Reichel used an algorithm of Gragg for unitary matrices to demonstrate that the class of matrices for which a practical conjugate gradient algorithm exists can be extended to include unitary and shifted unitary matrices. The implementation uses short double recursions for the direction vectors. This motivates the study of multiple recursion algorithms.
- Research Organization:
- Front Range Scientific Computations, Inc., Lakewood, CO (United States)
- OSTI ID:
- 440695
- Report Number(s):
- CONF-9604167--Vol.2; ON: DE96015307
- Country of Publication:
- United States
- Language:
- English
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