Page 272 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Sec. 8.10 Jacobi Diagonalization 259

INPUT MATRIX M
4.00000E+00 O.OOOOOE+00 O.OOOOOE+00
O.OOOOOE+00 2.00000E+00 O.OOOOOE+00
O.OOOOOE+00 O.OOOOOE+00 l.OOOOOE+00
INPUT MATRIX K
4.00000E+00 ~1.00000E+00 O.OOOOOE+00
-l.OOOOOE+00 2.00000E+00 “l.OOOOOE+00
O.OOOOOE+00 -l.OOOOOE+00 l.OOOOOE+00
[Q]« CHOLESKI DECOMP OF M
2.00000E+00 O.OOOOOE+00 O.OOOOOE+00
O.OOOOOE+00 1.41421E+00 O.OOOOOE+00
O.OOOOOE+00 O.OOOOOE+00 l.OOOOOE+00
[Q](INVERSE)
5.00000E-01 O.OOOOOE+00 O.OOOOOE+00
O.OOOOOE+00 7.07107E-01 O.OOOOOE+00
O.OOOOOE+00 O.OOOOOE+00 l.OOOOOE+00
[Q](INVERSE TRANSPOSE) X [K]
2.OOOOOE+00 -5.OOOOOE-01 O.OOOOOE+00
-7.07107E-01 1.41421E+00 -7.07107E-01
O.OOOOOE+00 -l.OOOOOE+00 l.OOOOOE+00
[A] - [Q](INVERSE TRANSPOSE) X [K] X [Q](INVERSE)
1.OOOOOE+00 -3.53553E-01 0.OOOOOE+00
-3.53553E-01 1.OOOOOE+00 -7.07107E-01
0.OOOOOE+00 -7.07107E-01 1.OOOOOE+00
ITERATION TRANSFORMATION OF [A]
INTERATION NUMBER ;
l.OOOOOE+00 -2.50000E-01 -2.50000E-01
-2.50000E-01 1.70711E+00 O.OOOOOE+00
-2.50000E-01 O.OOOOOE+00 2.92893E-01
INTERATION NUMBER 2
1.78657E+00 O.OOOOOE+00 -7.57264E-02
O.OOOOOE+00 9.20541E-01 -2.38255E-01
-7.57264E-02 -2.38255E-01 2.92893E-01
INTERATION NUMBER 3
1.78657E+00 2.41573E-02 -7.17698E-02
2.41573E-02 1.00074E+00 O.OOOOOE+00
-7.17698E-02 O.OOOOOE+00 2.12698E-01
INTERATION NUMBER 4
1.78983E+00 2.41323E-02 O.OOOOOE+00
2.41323E-02 1.00074E+00 1.09818E-03
O.OOOOOE+00 1.09818E-03 2.09432E-01
ACTUAL EIGEN VALUES OF [A] BASED ON 8 ITERATIONS
1.79057E+00 1.OOOOOE+00 2.0943iE-01
[Ul- EIGEN VECTORS OF [A] AS COLUMNS
3.16228E-01 8.94427E-01 3.16228E-01
-7.07107E-01 -4.43944E-08 7.07107E-01
6.32456E-01 -4.47214E-01 6.32456E-01
[X]« [Q](INVERSE) X [U] (ACTUAL PROBLEM EIGEN VECTORS)
1.58114E-01 4.47214E-01 1.58114E-01
-5.OOOOOE-Ol -3.13916E-08 5.OOOOOE-01
6.32456E-01 -4.47214E-01 6.32456E-01 Figure 8.10-3.