HP 48g Graphing Calculator - Manual (Page 181)

Determining the Accuracy of a Matrix Solution
There are two approaches to evaluating the accuracy of a computed
matrix solution when you suspect that you may be using singular or
ilhconditioned matrices:
■ Compute the residual array. This array is the result of substituting
the computed solution back into the original equation. The closer
the residual array is to being an array of zero elements, the more
accurate the solution.
B Use the condition nmnber. The condition number can be used to
estimate the number of accurate digits that can be expected using a
given matrix.
To find the residuals for a computed solution to a system of linear
equations (AX=B|:
1. Enter the array (vector or matrix) of constants (B) onto the stack.
2. Enter the matrix of coefficients (A).
3. Enter the computed solution array (must be of the same type and
dimensions as the constants array)(X).
4. Press either
(MTHI
M
h
T R
(NXT)
R S D (or
SOLVE)
S Y S
R S D ). The resulting array of residuals (AX-B) shows how close
the computed solution was to an actual solution—the smaller the
absolute value of the elements, the better the solution.
To approximate the number of accurate digits in a computed
soiutiOEi:
14
1. If the elements in the matrix A are exact, enter 15, the maximum
number of digits computed internally by the HP 48, onto the
stack. If the elements in matrix A were rounded to 12 digits (from
previous computations, for example), then enter 12.
2. Enter the matrix of coefficients (A).
3. Press
[MTH
1 M F i T R N O R M C O N D to find the condition number
of the matrix.
4. Press fr^(LOG ) |3 to find the approximate number of accurate
digits in a solution computed using the given matrix of coefficients.
This is merely a rough, rule-of-thumb estimate of a solution’s
accuracy and not a precise computation of it.
Matrices and Linear Algebra 14-17