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Rounding Errors in Solving Block Hessenberg Systems
Author(s):
Urs
von Matt;
G.
W.
Stewart.
Journal:
Math. Comp.
65
(1996),
115-135.
MSC (1991):
Primary 65G05;
Secondary 65F05
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Abstract:
A rounding error analysis is presented for a divide-and-conquer algorithm to solve linear systems with block Hessenberg matrices. Conditions are derived under which the algorithm computes a stable solution. The algorithm is shown to be stable for block diagonally dominant matrices and for M-matrices.
References:
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- ------, An updating algorithm for subspace tracking, IEEE Trans. Signal Processing 40 (1992), 1535--1541.
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- ------, Implementing an algorithm for solving block Hessenberg systems, Tech. Report CS-TR-3295, Department of Computer Science, University of Maryland, June 1994.
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- ------, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965.MR 32:1894
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Additional Information:
Urs
von Matt
Affiliation:
Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742
Email:
vonmatt@na-net.ornl.gov
G.
W.
Stewart
Affiliation:
Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, Maryland 20742
Email:
stewart@cs.umd.edu
DOI:
10.1090/S0025-5718-96-00667-9
PII:
S 0025-5718(96)00667-9
Keywords:
Rounding error analysis,
linear systems,
block Hessenberg matrices,
block diagonally dominant matrices,
M-matrices
Received by editor(s):
August 22, 1994
Received by editor(s) in revised form:
January 10, 1995
Additional Notes:
This work was supported in part by the National Science Foundation under grant CCR~9115568
Copyright of article:
Copyright
1996,
American Mathematical Society
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