HP 50g Graphing Calculator - Manual (Page 352)

Page 11-25
• If A is a square matrix and A is non-singular (i.e., it’s inverse matrix
exist, or its determinant is non-zero), LSQ returns the exact solution to
the linear system.
• If A has less than full row rank (underdetermined system of equations),
LSQ returns the solution with the minimum Euclidean length out of an
infinity number of solutions.
• If A has less than full column rank (over-determined system of
equations), LSQ returns the "solution" with the minimum residual value
e = A
⋅x – b. The system of equations may not have a solution,
therefore, the value returned is not a real solution to the system, just the
one with the smallest residual.
Function LSQ takes as input vector b and matrix A, in that order. Function LSQ
can be found in Function catalog (‚N). Next, we use function LSQ to
repeat the solutions found earlier with the numerical solver:
Square system
Consider the system
2x
1
+ 3x
2
–5x
3
= 13,
x
1
– 3x
2
+ 8x
3
= -13,
2x
1
– 2x
2
+ 4x
3
= -6,
with
The solution using LSQ is shown next:
.
6
13
13
, ,
4 2 2
8 3 1
5 3 2
3
2
1
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
− =
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
= b x A
and
x
x
x