Section 1.2 notes

[vgvreug]

• [x] Maybe add a bit more detail about the LU algorithm, just enough so that someone who's never heard of it can understand what's going on. Especially what u, ul, and ur represent since those are used a bunch later.
• [x] flop -> flops
• [x] About the speedup, did you run some code to get that 2.7 speedup or was it in one of the papers? If it was in a paper you need to cite it, and if you got that number yourself you should say that.
• [x] This line, delete "also" in "also the condition of A"
• [x] Missing word: "...the unit round-off is..." (again in next sentence)
• [x] Missing word: "...giving an even tighter bound of..."
• [ ] Is "strict and picky" a quote from the cited paper? If so it needs to be in quotes.
• [x] This line has an extra space after "line 4"
• [x] Here "Let" should be "and let"
• [ ] This line third sentence isn't making much sense, I'm really not sure what you're trying to say.
• [x] This line, third sentence: "Here the trade-off is the longer the Krylov subspace that is constructed..."
• [x] Same line, fifth sentence: delete "the" in "the returning to the outer loop"
• [x] Sixth sentence: delete "a" in "a low or no preconditioning" and "case" should be "cases"
• [x] This line fourth sentence: comma at the end should be a period.
• [x] Fifth sentence: "restrict" should be either "strict" or "restrictive"

[Gudauu]

• Is "strict and picky" a quote from the cited paper? If so it needs to be in quotes. It's actually my own wording. I have moved the citation to the preceding paragraph. Both these paragraphs are presenting their experiment results.
• This line third sentence isn't making much sense, I'm really not sure what you're trying to say. Honestly I couldn't understand it 100% either...I'm trying to represent the logic chain in chapter 7.2.1, page28 in this book. This conclusion is very important, and as I couldn't get it fully I pretty much preserved their wording. You may try rephrasing this one.

[vgvreug]

• If both paragraphs are talking about the paper we might want to put a citation at the end of both just to be safe? I don't know how much he'll take that into consideration though. The main reason I thought it might have been a quote is it just seemed tonally different from the rest of the paper.
• How about this: "It has been experimentally proven that adopting u = ul and ur=ug=up=u^2 results in phi aprox equal to xi, and therefore that xi approx equal to u as long as kappa(A) is not much larger than u^-1. These results indicate that the error…" With a citation at the end. Other than not having the symbols formatted, I think that's a bit easier to understand? What do you think?

[Gudauu]

Adopted.