HP HP-15C - Page 157

Section 4: Using Matrix Operations
155
This program uses inverse iteration to calculate an eigenvector qk
that corresponds to the eigenvalue kk such that ||qJ|_R = 1. The
technique uses an initial vector z^0) to calculate subsequent vectors
w*™) and z^"^ repeatedly from the equations
where s denotes the sign of the first component of w(" + ^ having
the largest absolute value. The iterations continue until z(n)
converges. That vector is an eigenvector qk corresponding to the
eigenvalue \.
The value used for \ need not be exact; the calculated eigenvector
is determined accurately in spite of small inaccuracies in A.&.
Furthermore, don't be concerned about having too accurate an
approximation to X^; the HP-15C can calculate the eigenvector
even when A — X^.1 is very ill-conditioned.
This technique requires that vector z(0) have a nonzero component
along the unknown eigenvector q^. Because there are no other
restrictions on z^, the program uses random components for z^.
At the end of each iteration, the program displays ||z*n + ^ — z^||#
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-1AP = diag(X1;X2,...).
Keystrokes
HllP/Rl
|T|CLEAR|PRGM
|RCL||MATRIX|[A"|
[STO] [MATRIX] [B]
|RCL||DIM|rAl
rsToio
|RCL|0
[STOll
Display
000-
001-42,21,13
002- 44 2
003-45,16,11
004-44,16,12
005-45,23,11
006- 44 0
007-42,21, 4
008- 45 0
009- 44 1
010- 45 12
Program mode.
Stores eigenvalue in R2
Stores A in B.