HP 50g Graphing Calculator User Manual

Page 352

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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

xb. 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

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