48/50 Linear System Solver

[Werner]

(01-14-2015 05:35 PM)Han Wrote:  Let A = [[12.25, 1.25, 4.5],[1.25,12.25,4.5],[4.5,4.5,3]]
Let b = [[-166.2],[157.2],[-3]]

Note that A is singular. On the HP48, with flag -22 SET (infinite -> MAXREAL), I get:

b A / -> x=[[-25.0333...],[4.3666...],[30]]
b A LSQ -> x=[[-14.972727...],[14.42727...],[-.1818...]]

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