Relative Perturbation Bounds for Matrix Eigenvalues and Singular Values

Author(s):  
Arnab Patra ◽  
P. D. Srivastava
SIAM Review ◽  
1989 ◽  
Vol 31 (1) ◽  
pp. 133-133
Author(s):  
Philip J. Davis

Author(s):  
Duanmei Zhou ◽  
Guoliang Chen ◽  
Guoxing Wu ◽  
Xiaoyan Chen

Acta Numerica ◽  
1998 ◽  
Vol 7 ◽  
pp. 151-201 ◽  
Author(s):  
Ilse C. F. Ipsen

It used to be good enough to bound absolute of matrix eigenvalues and singular values. Not any more. Now it is fashionable to bound relative errors. We present a collection of relative perturbation results which have emerged during the past ten years.No need to throw away all those absolute error bound, though. Deep down, the derivation of many relative bounds can be based on absolute bounds. This means that relative bounds are not always better. They may just be better sometimes – and exactly when depends on the perturbation.


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