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Early Termination over Small Fields II: On the Reliability of Block Krylov-Based Algorithms in a Generic Case

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Author
Eberly, Wayne
Accessioned
2014-07-15T16:06:00Z
Available
2014-07-15T16:06:00Z
Issued
2014-07-15
Other
Black box matrix computations, lookahead in biconditional Lanczos algorithms, early termination in Wiedemann algorithms, randomized algorithms, computations over finite fields
Subject
Algorithms
Performance
Reliability
Theory
Type
technical report
Metadata
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Abstract
Block Hankel matrices, generated according to a particular distribution, arise in the analysis of Block Wiedemann and Block Lanczos algorithms. It is shown that if the input matrix A has entries in a small finite field Fq and satisfies a condition that holds generically, then the expected nullities of these matrices are low — as needed to establish the efficiency and reliability of these algorithms. A sparse matrix preconditioner, that ensures that the above-mentioned condition holds with high probability, is also contributed.
Refereed
No
Corporate
University of Calgary
Faculty
Science
Doi
http://dx.doi.org/10.11575/PRISM/30587
Uri
http://hdl.handle.net/1880/50165
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