User Manual

120 Section 4: Using Matrix Operations
120
)row1(
),row1(
rows)(
*
p
q
*











00
0
gU
A
**
Where U
*
is also an upper-triangular matrix. You can obtain the solution b
(n+1)
to the
augmented system of p + 1 rows by solving






















*
)1(
1
q
q
n
0
b
0
gU
*
**
By replacing the last row of A* by r
n+2
and repeating the factorization, you can continue
including additional rows of data in the system. You can add rows indefinitely without
increasing the required storage space.
The program below begins with n = 0 and A = 0. You enter the rows r
m
successively for m =
1, 2, ..., p − 1 in turn. You then obtain the current solution b after entering each subsequent
row.
You can also solve weighted least-squares problems and linearly constrained least-squares
problems using this program. Make the necessary substitutions described under Orthogonal
Factorization earlier in this section.
Keystrokes
Display
|¥
Program mode.
´CLEAR M
000-
´bA
001-42,21,11
Program to input new row.
O2
002- 44 2
Stores weight in R
2
.
1
003- 1
O1
004- 44 1
Stores l = 1 in R
1
.
´b4
005-42,21, 4
lmA
006-45,23,11
®
007- 34
O0
008 44 0
Stores k = p + 2 in R
0
.
´b5
009-42,21, 5
l1
010- 45 1
¦
011- 31
l2
012- 45 2
*
013- 20
´UOA
014u 44 11
´U
t5
015- 22 5
t4
016- 22 4
´bB
017-42,21,12
Program to update matrix A.