jmorriso@fs0.ee.ubc.ca (John Paul Morrison) (03/06/90)
Is anyone out there interested in linear equations, in particular homogeneous equations? I have stumbled on a few techniques, that require very little or no prgramming to find the entire solution space to homogeneous and over/under determined systems. The HP gives only the trivial solution (0,0,..,0) to homogeneous equations. The HP can solve under/over determined systems, but you only get a single vector; and there are infinitely many solutions. Finding the entire solution set can be useful for finding eigenvectors if you have repeated eigenvalues, and for determining linear independence etc. I believe the techniques I've found work by taking advantage of the way the HP solves systems of equations. I will post my findings if there is any interest: I have a feeling that they are so simple that everyone else has already found them out. Please save me the embarrasment of posting old or trivial news by responding if you are interested. A little while back I responded to a plea for eigenvalue /vector methods. I responded with the SOLVER method that many others have discovered independently. He was interested in complex eigenvalues though. Well I dug around, and I found someone had programmed MULLER's method. I entered it, and after correcting all the typos (grrrr!) I was very disappointed: it may converge fairly quickly, ie few iterations, but there are so many steps needed that it ran quite slowly. Newton's method works in the complex plane, and it is simple. I wrote a program to iterate through and solve for complex roots by calculating the derivative numerically. This allows it to be used when the function is not known algebraically. So there you have it: eigenvectors, eigenvalues, linear systems, the whole works! Drop me a note, and I'll put all the details and code together. jpm jmorriso@ee.ubc.ca