Componentwise Perturbation Analysis of the QR Decomposition of a Matrix

Round 1

Reviewer 1 Report

Dear Editor

This paper is written excellent form point of scientific and grammatical view. Also, the paper consists of methods' analysis, numerical examples and comparison to other bounds, which are calculated in similar papers. So I think that this paper is complete and doesn't need to be revisions. So, I recommend it for publication without any further changes.

I just have a question about comparison part:

Why doesn't the author compare one example for all existing methods to show that his bounds is the best? 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The author studied the perturbation analysis of the QR decomposition using the method of splitting operators. Asymptotic component-wise perturbation bounds were derived under column scaling of the underlying matrices. Numerical illustrations were included. The paper is well-written, scientific structure is consecutive, and Matlab files show this step-by-step work. I recommend this study for publication.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The paper contains excellent work. It provides component- wise asymptotic and global perturbation bounds for all elements of the QR decomposition. It Illustrates his findings through examples, and shows the superiority of the obtained bounds. As far as I could check there are no mistakes. However, it is impossible for me to check numerical calculations. I recommend the publication of this work.

Author Response

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Author Response File: Author Response.pdf