Page 116 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

104 Chapter 3

A=E D E -1

Where ‘D’ is the diagonal matrix filled with Eigen values in the diagonal.

T
T
-1
2
Consider the computation of the matrix A =A A=EDE EDE =EDDE
2 T
=ED E

100 T
In general A 100 is using ED E

For the given matrix ‘A’, eigen matrix ‘E’ is computed as

E= 0.9315 -0.8421 and the diagonal matrix D is given as follows
0.3637 0.5393

D = 4.5616
0

0

0 .4384

100
100 -1
Therefore A is computed as ED E =

5.06471.0e+065 7.90871.0e+065

1.97721.0e+065 3.08751.0e+065

Note that if all the eigen values in the Diagonal matrix described above is
n
less than 1, the matrix A converges to the value zero when n tends to
infinity.

TH
7. DETERMINATION OF K ELEMENT
IN THE SEQUENCE

Let us consider the sequence 0, 1, 2, 3, 6, 11, 20, 37… in which fourth
element is the summation of three previous numbers. Fifth value is the
summation of 2, 3 and 4 value of the sequence and so on.