TY - GEN
T1 - Fast verification for respective eigenvalues of symmetric matrix
AU - Miyajima, Shinya
AU - Ogita, Takeshi
AU - Oishi, Shin'ichi
PY - 2005/12/1
Y1 - 2005/12/1
N2 - A fast verification algorithm of calculating guaranteed error bounds for all approximate eigenvalues of a real symmetric matrix is proposed. In the proposed algorithm, Rump's and Wilkinson's bounds are combined. By introducing Wilkinson's bound, it is possible to improve the error bound obtained by the verification algorithm based on Rump's bound with a small additional cost. Finally, this paper includes some numerical examples to show the efficiency of the proposed algorithm.
AB - A fast verification algorithm of calculating guaranteed error bounds for all approximate eigenvalues of a real symmetric matrix is proposed. In the proposed algorithm, Rump's and Wilkinson's bounds are combined. By introducing Wilkinson's bound, it is possible to improve the error bound obtained by the verification algorithm based on Rump's bound with a small additional cost. Finally, this paper includes some numerical examples to show the efficiency of the proposed algorithm.
UR - http://www.scopus.com/inward/record.url?scp=33744943311&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33744943311&partnerID=8YFLogxK
U2 - 10.1007/11555964_26
DO - 10.1007/11555964_26
M3 - Conference contribution
AN - SCOPUS:33744943311
SN - 3540289666
SN - 9783540289661
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 306
EP - 317
BT - Computer Algebra in Scientific Computing - 8th International Workshop, CASC 2005, Proceedings
T2 - 8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005
Y2 - 12 September 2005 through 16 September 2005
ER -