As part of my resolution to read some Numerical Analysis stuff this year, I read C. T. Kelly’s Iterative Methods for Linear and Nonlinear Systems. I can say with certainty, that on the surface I underestimated this book. I expected a thin book on iterative methods (it certainly has less pages than Nocedal and Wright or Yousef Saad’s book), but it certainly has some substance to it.
That being said, I would not recommend reading this cover-to-cover as I did, as there were certainly things that Kelly spent time on that I didn’t really grok by the end. In particular, there are a lot of details to the algebraic proofs, both tricks and repeated techniques that are easy to miss when not working through the proofs. As it was, I was primarily reading this on the bus, and didn’t really have pencil, paper, and space readily available to work through all the algebra.
Still, this book met my goal of thinking about Numerical Analysis again. While I don’t think I could run out and write some deep papers after this refresher, I at least have some ideas in my head of where to go next and how to think along those lines. I think my next endeavor will be to read through Iterative Methods of Optimization in a similar way – while it won’t be perfect, it’ll at least get me thinking.
This, in the end, was my primary goal, so the book was well worth the time. It’s also worth mentioning that I did like Kelly’s style and the book felt good to read. It also wasn’t overly long, so it made for a good book to read in the way that I was reading it.