48/50 Linear System Solver

[Han]

(01-15-2015 12:17 PM)Werner Wrote:  As I said before:
with flag -54 SET, both b A / and the linear solver application return x=[[-25.0333...],[4.3666...],[30]]. In this case, the 48 does not know A is singular - the computed determinant is 1.485e-12, and a result can be calculated using the normal LU decomposition and subsequent solve. Of course, COND returns 3.e15 meaning the result is meaningless.
with flag -54 CLEAR, b A / returns Infinite Result, and the solver app returns the Least Squares solution.

Cheers, Werner

Thank you, Werner. I don't know how I glossed over your original post and didn't see your comments -- probably had tunnel vision and too focused on something else. Your explanation is very helpful.

Edit: So I did the LU decomposition of the matrix, and got a different solution: [[84.9666...],[114.3666...],[-300]]. In original example posted by Tim:

Quote:With flag -54 Set (use tiny element), both methods will return

[ -5.41666..e14 -2.0833..e14 -1.25..e14]

Using LU, I got the same result. However, for my particular example, LU doesn't give the same answer as the / operator (under the same flag settings) which suggests that the HP48 doesn't seem to always use LU.

Just to be clear, I'm not so much after meaningful solutions as I am about understanding how the HP48 solves linear systems using the / operator. So far I've tried QR, LU, and pseudo-inverse (least squares) and none match. QR gives [ 139.27, -181.42, 5.43 ], LU gives something with large norm (useless answer), and least squares I already listed.