TY - JOUR
T1 - Fast enclosure of matrix eigenvalues and singular values via rounding mode controlled computation
AU - Oishi, Shin'ichi
PY - 2001/2/15
Y1 - 2001/2/15
N2 - Modifications of Bauer-Fike type and Weyl type perturbation theorems are presented for matrix eigenvalue and singular value problems. It is shown that the conditions of the presented theorems can be rigorously checked by floating point computation with rounding mode control. It is stressed that verification programs can be easily constructed on usual numerical softwares like MATLAB. Computational cost of obtaining rigorous error bounds for computed eigenvalues is shown to be 6n3 flops for a real symmetric n×n matrix.
AB - Modifications of Bauer-Fike type and Weyl type perturbation theorems are presented for matrix eigenvalue and singular value problems. It is shown that the conditions of the presented theorems can be rigorously checked by floating point computation with rounding mode control. It is stressed that verification programs can be easily constructed on usual numerical softwares like MATLAB. Computational cost of obtaining rigorous error bounds for computed eigenvalues is shown to be 6n3 flops for a real symmetric n×n matrix.
KW - Bauer-Fike type theorem
KW - Rounding mode controlled computation
KW - Verified eigenvalue computation
KW - Weyl type theorem
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U2 - 10.1016/S0024-3795(00)00272-X
DO - 10.1016/S0024-3795(00)00272-X
M3 - Article
AN - SCOPUS:0035630729
SN - 0024-3795
VL - 324
SP - 133
EP - 146
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 1-3
ER -