Solving a system of nonlinear equations – HP 15c User Manual
Page 102
102
Section 4: Using Matrix Operations
102
Example: Use the residual correction program to calculate the inverse of matrix A for
.
17
4
8
57
10
24
72
16
33
A
The theoretical inverse of A is
.
9
3
/
2
3
/
8
2
/
51
2
/
5
8
32
3
/
8
3
/
29
1
A
Find the inverse by solving AX = B for X, where B is a 3 × 3 identity matrix.
First, enter the program from above. Then, in Run mode, enter the elements into matrix A
(the system matrix) and matrix B (the right-hand, identity matrix). Press GA to
execute the program.
Recall the elements of the uncorrected solution, matrix C:
.
000000203
.
9
6666666836
.
0
666666728
.
2
50000055
.
25
500000046
.
2
000000167
.
8
00000071
.
32
666666726
.
2
666666881
.
9
C
This solution is correct to seven digits. The accuracy is well within that predicted by the
equation on page 88.
(number of correct digits) ≥ 9 – log(||A|| ||C||) – log (3) ≈ 4.8.
Recall the elements of the corrected solution, matrix B:
.
000000000
.
9
6666666667
.
0
666666667
.
2
50000000
.
25
500000000
.
2
000000000
.
8
00000000
.
32
666666667
.
2
666666667
.
9
B
One iteration of refinement yields 10 correct digits in this case.
Solving a System of Nonlinear Equations
Consider a system of p nonlinear equations in p unknowns:
f
i
(x
1
, x
2
, …, x
p
) = 0 for i = 1, 2, …, p
for which the solution x
1
, x
2
, … , x
p
is sought.