HP 15c - Manual (Page 131)

Section 4: Using Matrix Operations 131
The value used for λ
k
need not be exact; the calculated eigenvector is determined accurately
in spite of small inaccuracies in λ
k
. Furthermore, don't be concerned about having too
accurate an approximation to λ
k
; the HP-15C can calculate the eigenvector even when
A − λ
k
I is very ill-conditioned.
This technique requires that vector z
(0)
have a nonzero component along the unknown
eigenvector q
k
.. Because there are no other restrictions on z
(0)
, the program uses random
components for z
(0)
. At the end of each iteration, the program displays ||z
(n+1) − z (n)
||
R
to show
the rate of convergence.
This program can accommodate a matrix A that isn't symmetric but has a diagonal Jordan
canonical form−that is, there exists some nonsingular matrix P such that P
-1
AP= diag(λ
1
, λ
2
,
…).
Keystrokes Display
|¥
Program mode.
´CLEARM 000-
´bC 001-42,21,13
O2 002- 44 2 Stores eigenvalue in R
2
l>A 003-45,16,11
O>B 004-44,16,12 Stores A in B.
lmA 005-45,23,11
O0 006- 44 0
´b4 007-42,21, 4
l0 008- 45 0
O1 009- 44 1
lB 010- 45 12
l-2 011-45,30, 2
OB 012- 44 12 Modifies diagonal elements of
B.
´e0 013-42, 5, 0
t4 014- 22 4
lmA 015-45,23,11
1 016- 1
´mC 017-42,23,13 Dimensions C to n × 1.
´>1 018-42,16, 1
´b5 019-42,21, 5
´# 020- 42 36
´UOC´
U 021u 44 13 Stores random components in
C.
t5 022- 22 5
´b6 023-42,21, 6 Routine for iterating z
(n)
and
w
(n)
.