Good idea. The link should be "jwiki" rather than "wiki": http://www.jsoftware.com/jwiki/Essays/Eigenvalues
----- Original Message ----- From: "Sherlock, Ric" <[EMAIL PROTECTED]> Date: Monday, August 27, 2007 6:50 Subject: RE: [Jprogramming] Re: More on eigen values To: Programming forum <[email protected]> > I have made a first go at putting this post up as an essay on > the wiki > ... hope you don't mind John! > > Please feel free to tidy it up as required. > > http://www.jsoftware.com/wiki/Essays/Eigenvalues > > > -----Original Message----- > > From: [EMAIL PROTECTED] > > [mailto:[EMAIL PROTECTED] On Behalf Of John Randall > > Sent: Monday, 27 August 2007 23:43 > > To: Programming forum > > Subject: Re: [Jprogramming] Re: More on eigen values > > > > Roger Hui wrote: > > > eval1=: +/ .*&>/@|.&(128!:0) > > > > It is interesting to compare the various eigenvalue methods > > that have been proposed. > > > > NB. LAPACK > > > > require '~addons/math/lapack/lapack.ijs' > > require '~addons/math/lapack/dgeev.ijs' > > ev=:[: clean_jlapack_ 1 >@{ dgeev_jlapack_ > > > > NB. Iterative QR algorithm > > > > rheval=:+/ .*&>/@|.&(128!:0) NB. Roger Hui > > rh=: [: (<0 1)&|: rheval ^:_ > > > > mseval=:(>&(1&{) +/ .* >&(0&{))&(128!:0) NB. M. Shimura > > ms=:[: (<0 1)&|: mseval ^:_ > > > > > > NB. Leverrier-Faddeev Algorithm > > char=: 3 : 0 > > [EMAIL PROTECTED] > > for_k. >:i.n do. > > X=.y +/ . * X > > p=.p,pk=.-k%~+/(<0 1)|:X > > X=.X+pk*I > > end. > > |.p > > ) > > lf=:>@{:@[EMAIL PROTECTED] > > > > > > The LAPACK method is a direct method, but does preconditioning. > > > > The QR method is iterative, and so is able to get past small > > instabilities. > > > > Methods which find the characteristic polynomial, like the LF > > method, work well on small examples, but because of the > > instability of finding polynomial roots, may go wrong with > > large examples. > > > > dm=:[EMAIL PROTECTED]@# NB. diagonal matrix > > > > (-:[EMAIL PROTECTED]) >:i.20 > > 1 > > (-:[EMAIL PROTECTED]) >:i.20 > > 1 > > (-:[EMAIL PROTECTED]) >:i.20 > > 1 > > (-:[EMAIL PROTECTED]) >:i.20 > > 0 > > > > Best wishes, > > > > John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
