Calculating the Residual
The HP-15C enables you to calculate the residual, that is, the matrix
Residual = Rîš±YX
where R is the result matrix and X and Y are the matrices specified in the
X- and Y-registers.
This capability is useful, for example, in doing iterative refinement on the
solution of a system of equations and for linear regression problems. For
example, if C is a possible solution for AX = B, then B îš± AC indicates how
well this solution satisfies the equation. (Refer to the HP-15C Advanced
Functions Handbook for information about iterative refinement and linear
regression.)
The residual function (> 6) uses the current contents of the result
matrix and the matrices specified in the X- and Y-registers to calculate the
residual defined above. The residual is stored in the result matrix, replacing
the original result matrix. A matrix specified in the X- or Y-register can not
be the result matrix.
Using > 6 rather than * and - gives a result with improved
accuracy, particularly if the residual is small compared to the matrices being
subtracted.
To calculate the residual:
1. Enter the descriptor of the Y matrix into the Y-register.
2. Enter the descriptor of the X matrix into the X-register.
3. Designate the R matrix as the result matrix.
4. Press ´> 6. The residual replaces the original result
matrix (R). The descriptor of the result matrix is placed in the X-
register.
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