832
Appendix A: Functions and Instructions
QR
MATH/Matrix menu
QR
matrix
,
qMatName
,
rMatName[
,
tol]
Calculates the Householder QR factorization of a
real or complex
matrix
. The resulting Q and R
matrices are stored to the specified
MatNames
. The
Q matrix is unitary. The R matrix is upper triangular.
Optionally, any matrix element is treated as zero if
its absolute value is less than
tol
. This tolerance is
used only if the matrix has floating-point entries and
does not contain any symbolic variables that have
not been assigned a value. Otherwise,
tol
is ignored.
•
If you use
¥ ¸
or set the mode to
Exact/Approx=APPROXIMATE
, computations
are done using floating-point arithmetic.
•
If
tol
is omitted or not used, the default tolerance
is calculated as:
5
E
ë
14
ù
max(dim(
matrix
))
ù
rowNorm(
matrix
)
The floating-point number (9.) in
m1
causes
results to be calculated in floating-point form.
[1,2,3;4,5,6;7,8,9.]
!
m1
¸
1 2 3
4 5 6
7 8 9.
QR m1,qm,rm
¸
Done
qm
¸
.123… .904… .408…
.492… .301…
ë
.816…
.861…
ë
.301… .408…
rm
¸
8.124… 9.601… 11.078…
0. .904… 1.809…
0. 0. 0.
[m,n;o,p]
!
m1
¸
m n
o p
The QR factorization is computed numerically using
Householder transformations. The symbolic solution
is computed using Gram-Schmidt. The columns in
qMatName
are the orthonormal basis vectors that
span the space defined by
matrix
.
QR m1,qm,rm
¸
Done
qm
¸
m
m
2
+ o
2
ë
sign(m
ø
p
ì
n
ø
o)
ø
o
m
2
+ o
2
o
m
2
+ o
2
m
ø
sign(m
ø
p
ì
n
ø
o)
m
2
+ o
2
rm
¸
m
2
+ o
2
m
ø
n+o
ø
p
m
2
+ o
2
0
|
m
ø
p
ì
n
ø
o
|
m
2
+ o
2
QuadReg
MATH/Statistics/Regressions menu
QuadReg
list1
,
list2
[
,
[
list3
] [
,
list4
,
list5
]
]
Calculates the quadratic polynomial regression and
updates the system statistics variables.
All the lists must have equal dimensions except for
list5
.
list1
represents xlist.
list2
represents ylist.
list3
represents frequency.
list4
represents category codes.
list5
represents category include list.
In function graphing mode:
{0,1,2,3,4,5,6,7}
!
L1
¸
{1 2 3
...
}
{4,3,1,1,2,2,3,3}
!
L2
¸
{4 3 1
...
}
QuadReg L1,L2
¸
Done
ShowStat
¸
Summary of Contents for Titanium TI-89
Page 9: ...Getting Started 6 TI 89 Titanium keys Ë Ì Í Ê ...
Page 34: ...Getting Started 31 2 or D 2 B u s i n e s s D B D B Press Result ...
Page 43: ...Getting Started 40 3 0 D B D D B D Press Result ...
Page 44: ...Getting Started 41 D 2 0 0 2 D B Scroll down to October and press Press Result ...
Page 58: ...Getting Started 55 Example Set split screen mode to TOP BOTTOM Press Result 3 B D ...
Page 70: ...Getting Started 67 ...
Page 175: ...Operating the Calculator 172 From the Keyboard ...
Page 456: ...Tables 453 ...
Page 527: ...Data Matrix Editor 524 ...
