vgvreug
commented
4 months ago - [x] We should be consistent about whether the acronym or the full name goes in the parenthesis the first time it's used. My vote is that the acronym should be in parenthesis, but either is fine as long as we're consistent.
- [x] First sentence is kind of wordy and should probably be broken up to flow better. Maybe: "Generalized Minimal Residual Method (GMRES) and its variants are advanced numerical techniques for solving non-symmetric linear systems based on iterative refinement (IR). This method is particularly useful for..."
- [ ] Second sentence doesn't add much, it can be easily absorbed into a different sentence like I did above
- [ ] Are there other steps in a GMRES iteration? If not "include" should be changed to "are". As a side note this is somewhere where using a numbered list might be good, it would make it clear what the different steps are. But this is also a matter of opinion, either is probably fine.
- [ ] I think you missed a word, it should be "...using the Arnoldi process"
- [ ] Is there supposed to be a sub heading here? Right now it's kind of an abrupt transition from talking about the steps of a GMRES iteration to describing a linear system.
- [x] You have a comma at the end of this line that I think should be deleted.
- [x] On this line there a missing space that should be between A and r0, and again I don't think a comma is necessary at the end of the line.
- [x] This line is missing a word and has an extra capital letter: "and is unique, though it can be computed..."
- [x] Missing space here between "basis, called" and Krylov doesn't have an e on the end
- [x] Be consistent about punctuation. Either this line shouldn't start with a capital or the line above should have a period at the end. Also consistency about using capitals for the vectors in V1...Vn+1
- [x] That line also has a sentence fragment. "The initial vector s..." what about that vector?
- [x] Typo, "approximately". maybe run it through a spellchecker if wherever you're writing doesn't have one built in.
- [ ] This line should have "and" instead of a comma between the residual types. Second sentence should end with a comma and connect to the next line, currently it's a fragment.
- [x] Another typo, whilce -> while
- [ ] "GMRES has played a significant role" in what? Should probably expand on this.
- [ ] These two sentences say almost the same thing, the second one should probably be deleted.
Gudauu