Editing Arnoldi iteration (section)

==Restarted Arnoldi iteration==
Due to practical storage consideration, common implementations of Arnoldi methods typically restart after a fixed number of iterations. One approach is the Implicitly Restarted Arnoldi Method (IRAM)<ref>{{cite journal |author1=R. B. Lehoucq |author2=D. C. Sorensen |name-list-style=amp |year=1996 |title=Deflation Techniques for an Implicitly Restarted Arnoldi Iteration |journal=SIAM Journal on Matrix Analysis and Applications |volume=17 |issue=4 |pages=789–821 |doi=10.1137/S0895479895281484 |hdl-access=free |hdl=1911/101832}}</ref> by Lehoucq and Sorensen, which was popularized in the free and open source software package [[ARPACK]].<ref>{{cite web |author1=R. B. Lehoucq |author2=D. C. Sorensen |author3=C. Yang |name-list-style=amp |year=1998 |title=ARPACK Users Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods |url=http://www.ec-securehost.com/SIAM/SE06.html |url-status=dead |archive-url=https://web.archive.org/web/20070626080708/http://www.ec-securehost.com/SIAM/SE06.html |archive-date=2007-06-26 |access-date=2007-06-30 |publisher=SIAM}}</ref> Another approach is the Krylov-Schur Algorithm by G. W. Stewart, which is more stable and simpler to implement than IRAM.<ref>{{Cite journal |last=Stewart |first=G. W. |date=2002 |title=A Krylov--Schur Algorithm for Large Eigenproblems |url=http://epubs.siam.org/doi/10.1137/S0895479800371529 |journal=SIAM Journal on Matrix Analysis and Applications |language=en |volume=23 |issue=3 |pages=601–614 |doi=10.1137/S0895479800371529 |issn=0895-4798}}</ref>