Analysis of krylov subspace methods

mb.pejvak · November 17, 2019, 04:07

i am looking up on internet to find a resource in which Fourier analysis of krylov subspce method (CG, GMRES method) were studied. Can anyone introduce a reference in which the topic was explained.

wangsen992 · November 18, 2019, 03:23

Those are general discussed in computational methods for linear algebra, particularly in iterative methods. What I think was pretty helpful for me to grab a decent understanding in those concepts is a book "A First Course in Numerical Methods" by Ascher & Greif, in Chapter 7. It was pretty fundamental and basic, and it didn't really touch on more advanced methods such as bi-conjugate and multigrid is very briefly touched. But overall I think it is a pretty good introductory text on those you've mentioned.

mb.pejvak · November 21, 2019, 01:40

@wangsen992 Thanks for your recommendation. I found a paper in which convergence of GMRES was studied and it has also some reference to other papers which did the same for other methods in Krylov subspace.

The paper can be found here:

wangsen992 · November 21, 2019, 02:51

@mb.pejvak Thanks for the reference to the Krylov Subspace Methods. I will definitely check them out! Cheers!

praveen · November 21, 2019, 03:38

Book of Y Saad is great, you can get a pdf here

https://www-users.cs.umn.edu/~saad/I...Book_2ndEd.pdf

and will contain what you are looking for.

November 17, 2019, 04:07	Analysis of krylov subspace methods	#1
mb.pejvak Senior Member Mehdi Babamehdi Join Date: Jan 2011 Posts: 158 Rep Power: 15	i am looking up on internet to find a resource in which Fourier analysis of krylov subspce method (CG, GMRES method) were studied. Can anyone introduce a reference in which the topic was explained.

November 21, 2019, 03:38		#5
praveen Super Moderator Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 343 Blog Entries: 6 Rep Power: 18	Book of Y Saad is great, you can get a pdf here https://www-users.cs.umn.edu/~saad/I...Book_2ndEd.pdf and will contain what you are looking for. __________________ http://cpraveen.github.io http://twitter.com/cfdlab http://github.com/cpraveen

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November 18, 2019, 03:23		#2
wangsen992 New Member Sen Wang Join Date: Jul 2018 Location: Singapore / Notre Dame, U.S. Posts: 20 Blog Entries: 1 Rep Power: 8	Those are general discussed in computational methods for linear algebra, particularly in iterative methods. What I think was pretty helpful for me to grab a decent understanding in those concepts is a book "A First Course in Numerical Methods" by Ascher & Greif, in Chapter 7. It was pretty fundamental and basic, and it didn't really touch on more advanced methods such as bi-conjugate and multigrid is very briefly touched. But overall I think it is a pretty good introductory text on those you've mentioned.

November 21, 2019, 01:40		#3
mb.pejvak Senior Member Mehdi Babamehdi Join Date: Jan 2011 Posts: 158 Rep Power: 15	@wangsen992 Thanks for your recommendation. I found a paper in which convergence of GMRES was studied and it has also some reference to other papers which did the same for other methods in Krylov subspace. The paper can be found here:

November 21, 2019, 02:51		#4
wangsen992 New Member Sen Wang Join Date: Jul 2018 Location: Singapore / Notre Dame, U.S. Posts: 20 Blog Entries: 1 Rep Power: 8	@mb.pejvak Thanks for the reference to the Krylov Subspace Methods. I will definitely check them out! Cheers!