F08XEF Example Program Results Matrix A after balancing 1 2 3 4 5 1 1.0000 1.0000 0.1000 0.1000 0.1000 2 2.0000 4.0000 0.8000 1.6000 3.2000 3 0.3000 0.9000 0.2700 0.8100 2.4300 4 0.4000 1.6000 0.6400 2.5600 10.2400 5 0.5000 2.5000 1.2500 6.2500 31.2500 Matrix B after balancing 1 2 3 4 5 1 1.0000 2.0000 0.3000 0.4000 0.5000 2 1.0000 4.0000 0.9000 1.6000 2.5000 3 0.1000 0.8000 0.2700 0.6400 1.2500 4 0.1000 1.6000 0.8100 2.5600 6.2500 5 0.1000 3.2000 2.4300 10.2400 31.2500 Matrix A in Hessenberg form 1 2 3 4 5 1 -2.1898 -0.3181 2.0547 4.7371 -4.6249 2 -0.8395 -0.0426 1.7132 7.5194 -17.1850 3 0.0000 -0.2846 -1.0101 -7.5927 26.4499 4 0.0000 0.0000 0.0376 1.4070 -3.3643 5 0.0000 0.0000 0.0000 0.3813 -0.9937 Matrix B is triangular 1 2 3 4 5 1 -1.4248 -0.3476 2.1175 5.5813 -3.9269 2 0.0000 -0.0782 0.1189 8.0940 -15.2928 3 0.0000 0.0000 1.0021 -10.9356 26.5971 4 0.0000 0.0000 0.0000 0.5820 -0.0730 5 0.0000 0.0000 0.0000 0.0000 0.5321 Minimal required LWORK = 5 Actual value of LWORK = 30 Generalized eigenvalues 1 ( -2.437, 0.000) 2 ( 0.607, 0.795) 3 ( 0.607, -0.795) 4 ( 1.000, 0.000) 5 ( -0.410, 0.000)