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HP HP-15C Advanced Functions Handbook

HP HP-15C
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114
Section
4:
Using
Matrix
Operations
The
upper-triangular matrix
U and the
product
Qy can be
written
as
u=
(p
rows)
(n
—prows)
and
Qy
=
(p
rows)
(n p
rows)
Then
UHlQrllJ
HiQy-Ub||£
>
Ml
with equality when
g
Ub = 0. In
other words,
the
solution
to the
ordinary least-squares problem
is any
solution
to Ub
g and the
minimal
sum of
squares
is
\\f\\p.
This
is the
basis
of all
numerically
sound least-squares programs.
You
can
solve
the
unconstrained least-squares problem
in two
steps:
1.
Perform
the
orthogonal factorization
of the
augmented
n X (p + 1)
matrix
=
QTV
where
Q
=
Q
l,
and
retain
only
the
upper-triangular factor
V,
which
you can
then
partition
as
U
g
0 q
0 0
(p
rows)
(1
row)
(n
p 1
rows)
A
T.
(1
column)
1
(p
columns)
Only
the
first
p + 1
rows (and columns)
of V
need
to be
retained. (Note
that
Q
here
is not the
same
as
that
mentioned
earlier, since
this
Q
must also transform
y.)

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HP HP-15C Specifications

General IconGeneral
BrandHP
ModelHP-15C
CategoryCalculator
LanguageEnglish

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