The Lanczos algorithm with partial reorthogonalization

without computing the inner products. Based on the information from the recurrence, reorthogonalizations occur only when necessary. Thus substantial savings are made as compared to FRO. In some numerical examples we apply the Lanczos algorithm with PRO to the solution of large symmetric systems of l...

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Bibliographic Details
Published in:Mathematics of computation 1984-01, Vol.42 (165), p.115-142
Main Author: Simon, Horst D.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Eigenvalues
Eigenvectors
Exact sciences and technology
Inner products
Linear equations
Linear systems
Mathematical vectors
Mathematics
Matrices
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Orthogonality
Sciences and techniques of general use
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Summary:without computing the inner products. Based on the information from the recurrence, reorthogonalizations occur only when necessary. Thus substantial savings are made as compared to FRO. In some numerical examples we apply the Lanczos algorithm with PRO to the solution of large symmetric systems of linear equations and show that it is a robust and efficient algorithm for maintaining semiorthogonality among the Lanczos vectors. The results obtained compare favorably with the conjugate gradient method.]]>
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-1984-0725988-X