HP HP-15C Advanced Functions Handbook

Section 4: Using Matrix Operations 111
However, the normal equations are very sensitive to rounding
errors. (Orthogonal factorization, discussed on page 113, is
relatively insensitive to rounding errors.)
The weighted least-squares problem is a generalization of the
ordinary least-squares problem. In it you seek to minimize
n
HWr|||= X>?r?
where W is a diagonal n X n matrix with positive diagonal
elements wlt w2, ..., wn.
Then
||Wr||| = (y - Xb)rWrW(y - Xb)
and any solution b also satisfies the weighted normal equations
These are the normal equations with X and y replaced by WX and
Wy. Consequentially, these equations are sensitive to rounding
errors also.
The linearly constrained least-squares problem involves finding b
such that it minimizes
MIHIy-
subject to the constraints
Cb = d
/ *
Z^A
V=i
= dt for i — 1, 2,..., ml .
This is equivalent to finding a solution b to the augmented normal
equations
XrX CT
C 0
where 1, a vector of Lagrange multipliers, is part of the solution but
isn't used further. Again, the augmented equations are very
sensitive to rounding errors. Note also that weights can also be
included by replacing X and y with WX and Wy.

HP HP-15C Specifications

General

Brand	HP
Model	HP-15C
Category	Calculator
Language	English