METODO DE BAIRSTOW - EJEMPLO.pdf

SOLUCIONES NUMERICAS PARA INGENIERIA

MÉTODO DE BAIRSTOW EJEMPLO

DETERMINE LAS RAICES DEL POLINOMIO 1RA ITERACIÓN a5 a4 1

a3

bn

1

cn

1

-7 1 0 -6 1 0 -5

5 -6

-6 dr 1 ds

2NDA ITERACIÓN a5 a4 1 -7 2.8709 2.87097 7 0 bn 1 -4.12903 2.87097 2.87097 0 cn 1 -1.25806

a1 -1 5 -6 -2 1 -5 -6

a0 7 -2 5 10 -6 1 5

2 dr -10 ds

a3

a2

a1

10 -11.85 -11.8543 43 2.22 2.2258 581 1 0. 0.37149 -3.61186 -3.61186 2.225 2.22581 81 -1.01457

-1 1.0665 1.06653 3 -9. -9.19 1904 043 3 -9.1239 -2.91279 -2.91279 -2.80 -2.80021 021 -14.8369

7 -26.1 -26.1944 944 0.82 0.8268 686 6 -18.3676 -42.5963 -42.5963 -2.2 -2.2582 5823 3 -63.222

-63.222 -14.8369 dr -14.8369 -1.01457 ds 3ERA ITERACIÓN a5 a4 1 -7 1.66 1.6640 405 5 0 bn 1 -5.33595 1.66405 1.66405 0 cn 1 -3.67189

  =   − 7  + 10  −   + 7 − 10

a2 10 -6 1 5 -5 1 1

UNIVERSIDAD TECNOLOGICA DE PANAMA

83.0407 dr 18.3676 ds

-10 10 -2 -2 5 -6 -3

1.87097 ea 1.22581

1

1

65.1685 55.0725

a0 -10 2.87097 2.22581 -52.73 -52.7326 26 -20. -20.30 308 8 -83.0407 -181.508 -181.508 -33.02 -33.0241 41 -297.573

-1.20691 ea -0.45408

72.5285 -25.6291

a3

a2

a1

a0

10 -8.8 -8.879 793 3 1.771 1.77173 73 2. 2.89243 -6.11023 -6.11023 1.771 1.77173 73 -1.44607 607

-1 4.81 4.8131 315 5 -9.45 -9.45384 384 -5.64069 -2.40634 -2.40634 -6.50 -6.50559 559 -14. 14.5526

7 -9.38 -9.3864 641 1 5.1245 5.12459 9 2. 2.73818 -24.2164 -24.2164 -2.5 -2.5620 6205 5 -24.0402

-10 1.66405 1.77173 4.55 4.5564 648 8 -9.9937 -9.99377 7 -15.4373 -40.0042 -40.0042 -25.78 -25.7833 33 -81. 81.2248

-24.0402 -14.5526 dr -14.5526 -1.44607 ds

15.4373 dr -2.73818 ds

0.35122 ea -1.64099

17.4279 -1255.16

PROF. :R.ELIZONDO


4TA ITERACIÓN a5 a4 1 -7 2.01527 0 bn 1 -4.98473 2.01527 0 cn 1 -2.96945

a3

a2

a1

10 -10.0456 0.13074 0.08515 -5.98426 0.13074 -5.76837

-1 0.17161 -0.6517 -1.48009 -11.6248 -0.38823 -13.4932

7 -2.9828 0.01113 4.02834 -27.1924 -0.75416 -23.9182

-23.9182 -13.4932 dr -13.4932 -5.76837 ds 5TA ITERACIÓN a5 a4 1

bn

cn


a3

2.07531 dr -4.02834 ds

a2

a1

a0 -10 2.01527 0.13074 8.1182 -0.19351 -2.07531 -48.2017 -1.76409 -52.0411 1.50412 ea -2.82004


26.1002 dr 11.4685 ds

a3

a2

10 -11.975 -1.64371 -3.61868 -3.12098 -1.64371 -8.38336

-1 -10.7676 6.615 -5.15262 -24.9453 1.72403 -28.3738

-73.0323 -28.3738 dr -28.3738 -8.38336 ds

a1 7 -15.332 5.94806 -2.3839 -84.4282 13.7798 -73.0323

8.62403 dr 2.3839 ds

42.7381 104.861

a0

-7 10 -1 7 -10 3.5194 -12.2496 -17.382 -31.7507 -40.3621 0 -2.6893 9.36039 13.2822 24.2619 1 -3.4806 -4.93892 -9.02164 -11.4685 -26.1002 3.5194 0.13652 -26.3663 -124.911 -409.067 0 -2.6893 -0.10432 20.1474 95.4492 1 0.03879 -7.4917 -35.4922 -116.232 -339.718

-116.232 -35.4922 dr -35.4922 -7.4917 ds


-0.54383 ea 1.04559

3.5194

-2.6893

18.2765 -63.6116

a0 -10 2.97557 -1.64371 -7.09344 8.46941 -8.62403 -217.312 46.6383 -179.298 0.02416 ea -0.36612

0.80535 18.2167

PROF. :R.ELIZONDO




a3

a2

10 -11.9997 -2.00983 -4.00956 -3.00138 -2.00983 -9.02077

-1 -12.0276 8.03989 -4.98768 -27.0598 2.01094 -30.0366

-71.8743 -30.0366 dr -30.0366 -9.02077 ds 8VA ITERACIÓN a5 a4 1 -7 2.99999 0 bn 1 -4.00001 2.99972 0 cn 1 -1.00028

a1

a0

7 -14.9617 8.05855 0.09689 -90.1014 18.1303 -71.8743

-0.31504 dr -0.09689 ds

a3

a2

10 -12 -1.99999 -3.99998 -3.00057 -2.00983 -9.01039

-1 -11.9999 7.99997 -4.99995 -27.0287 2.0104 -30.0182

-71.9369 -30.0182 dr -30.0182 -9.01039 ds

1 1

-7 2 -5 1 -4

a1

-1 0 -1 -4 -5

0.00896 -0.49228

a0

7 -14.9998 7.99992 0.00011 -90.0464 18.1094 -71.9369

-0.00016 dr -0.00011 ds

10 -10 0 -4 -4

-10 2.99972 -2.00983 0.29063 10.0244 0.31504 -215.603 60.3685 -154.919 0.00027 ea 0.00985

-10 2.99999 -1.99999 0.00032 9.99984 0.00016 -215.791 60.3317 -155.459 6.9E-06 ea -1.1E-05

DE LA SOLUCION DE LA CUADRATICA a 1 b -3 c 2 RAIZ 1 1 RAIZ2 2

1


0.00023 0.00055

las raices son reales

7 -2 5 -5 0

-10 10 0

2 1

POLINIOMIO DE DEFLACIÓN f3(x)=   − 4  − 4x-5

PROF. :R.ELIZONDO


1RA ITERACIÓN a3 a2 1


a1 -4 0

bn

1

-4 0

cn

1

-4

-2 -4

-4 dr 1 ds


a0 -4 0 1 -3 0 1 -2

-5 0 -4 -9 0 -4 -13

9 dr 3 ds

0

1

-1.16667 ea -1.66667

100 250

2NDA ITERACIÓN 1

bn

cn

-4 -4 -1.16667 6.02778 -0.66667 1 -5.16667 1.36111 -1.16667 7.38889 -0.66667 1 -6.33333 8.08333

8.08333 -6.33333 dr -6.33333 1 ds

-5 -1.16667 -0.66667 -1.58796 3.44444 -3.14352 -9.43056 4.22222 -8.35185

3.14352 dr -1.36111 ds

0.171 ea -0.27809

17.1748 29.4352

3ERA ITERACIÓN a3 a2 a1 a0 1 -4 -4 -5 -0.99566 -0.94476 -0.99566 4.974 -0.02912 -0.94476 4.71969 bn 1 -4.99566 0.02924 -0.30942 -0.99566 5.96535 -5.02793 -0.94476 5.66035 cn 1 -5.99133 5.04983 0.323

5.04983 -5.99133 dr -5.99133 1 ds

0.30942 dr -0.02924 ds

-0.00435 ea -0.05531

0.43514 5.53091

PROF. :R.ELIZONDO




4TA ITERACIÓN a3 a2 a1 a0 1 -4 -4 -5 -1.00001 -1.00007 -1.00001 5.00009 -1.9E-05 -1.00007 5.00037 bn 1 -5.00001 1.9E-05 0.00035 -1.00001 6.00012 -5.00014 -1.00007 6.00045 cn 1 -6.00003 5.00007 1.00066 5.00007 -6.00003 dr -6.00003 1 ds 5TA ITERACIÓN a3 a2 1

a1 -4 -1

1

-5 -1

cn

1

-6

5 -6

-6 dr 1 ds

bn

1

-5 -1

cn

1

-6

5 -6

-6 dr 1 ds

-1

-5.5E-10 dr -2.2E-10 ds

a1 -4 -1

1.5E-05 ea 7.1E-05

0.00149 -0.00706

a0

-4 -5 5 -2.2E-10 -1 5 2.2E-10 5.5E-10 6 -5 -1 6 5 1

bn

6TA ITERACIÓN a3 a2 1

-0.00035 dr -1.9E-05 ds

-1

6.1E-11 ea 1.4E-10

6.1E-09 -1.4E-08

a0 -4 5 -1 0 6 -1 5

-5 0 5 0 -5 6 1 0 dr 0 ds

-1

-1

0 ea 0

0 0

PROF. :R.ELIZONDO


7TA ITERACIÓN a3 a2 1

a1 -4 -1

1

-5 -1

cn

1

-6

5 -6

-6 dr 1 ds

bn

1

-5 -1

cn

1

-6

5 -6

-6 dr 1 ds

-5 0 5 0 -5 6 1

-1

0 dr 0 ds

a1 -4 -1


a0 -4 5 -1 0 6 -1 5

bn

8VA ITERACIÓN a3 a2 1


-1

0 ea 0

0 0

a0 -4 5 -1 0 6 -1 5

-5 0 5 0 -5 6 1 0 dr 0 ds

DE LA SOLUCION DE LA CUADRATICA a 1 b 1 c 1 RAIZ 1 -0.5 0.86603 RAIZ2 -0.5 -0.86603

-1

-1

0 ea 0

0 0

las raices son complejas

NOTA: ESTA ES UNA DIVISION SINTETICA DE NUMEROS COMPLEJOS 1 -4 -4 -5 -0.5 0.86603 1.5 -4.33013 5 1 -4.5 0.86603 -2.5 -4.33013 0 -0.5 -0.86603 2.5 4.33013 0 1 -5 0 0 0 0

0 0 0 0

-0.5

0.8660254

-0.5

-0.86603

POLINIOMIO DE DEFLACIÓN f1(x)=  − 5

PROF. :R.ELIZONDO

METODO DE BAIRSTOW - EJEMPLO.pdf

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