Don, I would reiterate what Henry has said about this problem. If you are trying it you should at least have a very careful read of the material in Numerical Recipes. You may find enough there to solve some problems.
If you are going to persist you should begin by clarifying what class of matrices you want to develop your calculations for. NR provides some groups of interest. Then explore the detailed transformations which are required, and ways of ensuring that they do not suffer from serious rounding problems The difficulty with most of the methods is that they depend on a sequence of steps operating on small subsets of the cells and they do not generalise readily to the larger scale array operations for which J is especially well suited. It is well worth understanding enough of the methods to appreciate the enormous effort which has gone into tuning the LAPACK routines. Enjoy the exercise. Fraser ----- Original Message ----- From: "Don Guinn" <dongu...@gmail.com> To: "Programming forum" <programming@jsoftware.com> Sent: Sunday, February 05, 2012 6:03 PM Subject: Re: [Jprogramming] Eigen or Eigan? > My idea was not to build the best method for finding Eigenvalues and > Eigenvectors, but to understand them. The trouble with using LAPACK > without > understanding is not the way to learn. Neither is studying LAPACK > productive in that rather than understanding the theory all effort is > spent > learning how LAPACK avoids numerical approximations forced by the limited > precision of computers. > > I wanted to apply the method for calculating Eigenvalues as described in > text books. Only use J notation instead of standard mathematical notation. > As a side effect the result is a J script that can calculate Eigenvalues. > It is will known that p. does not do well for large polynomials, but using > p. allows one to follow the theory of Eigenvalues without getting bogged > down on how to factor polynomials. > > What frustrated me was that I could not find any information on > calculating > Eigenvectors. So I posted my struggle to handle Eigenvectors looking for > advice. I appreciate the help given to me so far. I have found Gilbert > Strang's book and will read it. Also found this afternoon that Khan has > lectures on Eigenvalues and Eigenvectors. I look forward to studying them. > > Personally I think that J can so closely match textbook mathematical > notation is neat and its ability to do polynomial arithmetic so easily > shows the unique power of J. > > On Sat, Feb 4, 2012 at 4:51 PM, Henry Rich <henryhr...@nc.rr.com> wrote: > >> Agreed, and note that solving the characteristic polynomial is NOT used >> for finding eigenvalues of any but the smallest systems. *Numerical >> Recipes*, which generally thinks that any citizen can write their own >> code to do almost anything, suggests that you leave eigenvalues to >> LAPACK. >> >> Henry Rich >> >> On 2/3/2012 10:00 PM, Kip Murray wrote: >> > For applications get a copy of Gilbert Strang's Introduction to Linear >> > Algebra and read his Chapter 6 Eigenvalues and Eigenvectors. The bad >> > news is, this chapter starts on page 274. You are expected to >> > understand why he calls 2 2 $ 0.5 a projection matrix and 2 2 $ 0 1 1 0 >> > a reflection matrix. The good news is, he never forgets applications, >> > and his presentation of the math is first rate: "I try to explain >> > rather >> > than to deduce." You begin to respect eigenvalues and eigenvectors >> > when >> > you see their application to systems of differential equations in >> > section 6.3. >> > >> > On 2/3/2012 5:03 PM, Don Guinn wrote: >> >> >> >> I would appreciate comments and suggestions and where to go to better >> >> understand the applications of Eigenvalues and Eigenvectors. >> >> ---------------------------------------------------------------------- >> >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- >> > For information about J forums see http://www.jsoftware.com/forums.htm >> > >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
