Relative Perturbation Bounds for Matrix Eigenvalues and Singular Values

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Arnab Patra ◽  
P. D. Srivastava
Keyword(s):  
Singular Values ◽  
Perturbation Bounds ◽  
Matrix Eigenvalues

Perturbation Bounds for Matrix Eigenvalues (Rajendra Bhatia)

SIAM Review ◽  
1989 ◽  
Vol 31 (1) ◽  
pp. 133-133
Author(s):  
Philip J. Davis
Keyword(s):  
Perturbation Bounds ◽  
Matrix Eigenvalues

scholarly journals Perturbation bounds for eigenvalues of diagonalizable matrices and singular values

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Duanmei Zhou ◽  
Guoliang Chen ◽  
Guoxing Wu ◽  
Xiaoyan Chen
Keyword(s):  
Singular Values ◽  
Perturbation Bounds

scholarly journals Relative perturbation results for matrix eigenvalues and singular values

Acta Numerica ◽  
1998 ◽  
Vol 7 ◽  
pp. 151-201 ◽  
Author(s):  
Ilse C. F. Ipsen
Keyword(s):  
Error Bound ◽  
Singular Values ◽  
Absolute Error ◽  
The Past ◽  
Matrix Eigenvalues ◽  
Relative Errors

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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