12
ECUACIONES 5X + 2Y + -3 Z = 16.9 1X + -7Y + 1Z = -16.2 2X + 3Y + 5Z = 1.9 x°=

Gauss Seidel

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métodos numericos

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Page 1: Gauss Seidel

ECUACIONES5 X + 2 Y + -3 Z = 16.91 X + -7 Y + 1 Z = -16.2 12 X + 3 Y + 5 Z = 1.9 3 Ɛ=

-2x°=

Page 2: Gauss Seidel

K X* Y* Z* |Y*-Y*`| |Z*-Z*`|0 1 3 -2 0 0 01 0.98 2.16857143 -1.31314286 0.02 0.83142857 -0.68685714

0.05 2 1.72468571 2.37307755 -1.73372082 -0.74468571 -0.20450612 0.420577963 1.39053649 2.26525938 -1.53537023 0.33414922 0.10781817 -0.198350594 1.55267411 2.3167577 -1.63112426 -0.16213762 -0.05149832 0.095754045 1.47462236 2.2919283 -1.58500592 0.07805175 0.0248294 -0.04611834

|X*-X*`|

Page 3: Gauss Seidel

ECUACIONES10 X + -1 Y + 2 Z + 0 T = 6-1 X + 11 Y + -1 Z + 3 T = 25 12 X + -1 Y + 10 Z + -1 T = -11 2 Ɛ=0 X + 3 Y + -1 Z + 8 T = 15 -1

1

x°=

Page 4: Gauss Seidel

K X* Y* Z* |Y*-Y*`| |Z*-Z*`|0 1 2 -1 1 0 0 01 1.00000 2.00000 -1.00000 1.00000 0.00000 0.00000 0.00000

0.05 2 1.98000 2.45429 -1.88457 -0.98000 -0.45429 0.884573 1.26754 2.22614 -1.46270 0.71246 0.22815 -0.421874 1.61192 2.33560 -1.66613 -0.34438 -0.10946 0.203435 1.44608 2.28285 -1.56814 0.16584 0.05275 -0.09799

|X*-X*`|

Page 5: Gauss Seidel

|Z*-Z*`|0

0.000001.000000.000000.000000.00000

Page 6: Gauss Seidel

x y ecuaciones A X B1 3 3 = a + b* 1 1 1 32 5 5 = a + b* 2 1 2 a 5

1.5 4 4 = a + b* 1.5 1 1.5 x b = 43 6 6 = a + b* 3 1 3 6

3.7 5 5 = a + b* 3.7 1 3.7 5

Relación funcionaly=a+bx

y= 2.76 + 0.82 x

pares ẍ

Page 7: Gauss Seidel

k X ob Y ob Y cal Ɛi1 1 3 3.58 0.582 2 5 4.4 -0.63 1.5 4 3.99 -0.014 3 6 5.22 -0.785 3.7 5 5.794 0.794

Page 8: Gauss Seidel

x y ecuaciones A X B0 1.5 0.41 = a * 0 + ln(c) 0 1 0.40546511 1.25 0.22 = a * 1 + ln(c) 1 1 a 0.22314362 3.5 1.25 = a * 2 + ln(c) 2 1 x b = 1.2527633 5 1.61 = a * 3 + ln(c) 3 1 1.60943794 7.5 2.01 = a * 4 + ln(c) 4 1 2.014903

Relación funcional

aplicando lnln (y)=ax+lnC

y= 0.06364653 *x + 0.2569128ln(Y)= yx= xln(C)= b

pares ẍ

y=Ceᵃˣ

Page 9: Gauss Seidel

k X ob Y ob Y cal Ɛi1 0 1.5 0.25691275 -1.243087252 1 1.25 0.32055928 -0.929440723 2 3.5 0.38420582 -3.115794184 3 5 0.44785235 -4.552147655 4 7.5 0.51149888 -6.98850112