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Metode Numerik 2 - Universitas Indonesia

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Dari sistem persamaan linear:<br />

)<br />

f(x<br />

c<br />

bx<br />

ax<br />

)<br />

f(x<br />

c<br />

bx<br />

ax<br />

)<br />

f(x<br />

c<br />

bx<br />

ax<br />

1<br />

i<br />

1<br />

i<br />

2<br />

1<br />

i<br />

i<br />

i<br />

2<br />

i<br />

1<br />

-<br />

i<br />

1<br />

-<br />

i<br />

2<br />

1<br />

-<br />

i<br />

+<br />

+<br />

+<br />

=<br />

+<br />

+<br />

=<br />

+<br />

+<br />

=<br />

+<br />

+<br />

diperoleh:<br />

)<br />

x<br />

)(x<br />

x<br />

(x<br />

)<br />

)f(x<br />

x<br />

(x<br />

)<br />

x<br />

)(x<br />

x<br />

(x<br />

)<br />

)f(x<br />

x<br />

(x<br />

)<br />

x<br />

)(x<br />

x<br />

(x<br />

)<br />

)f(x<br />

x<br />

(x<br />

b<br />

)<br />

x<br />

)(x<br />

x<br />

(x<br />

)<br />

f(x<br />

)<br />

x<br />

)(x<br />

x<br />

(x<br />

)<br />

f(x<br />

)<br />

x<br />

)(x<br />

x<br />

(x<br />

)<br />

f(x<br />

a<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

i<br />

1<br />

-<br />

i<br />

1<br />

i<br />

i<br />

1<br />

i<br />

i<br />

i<br />

1<br />

i<br />

1<br />

-<br />

i<br />

1<br />

i<br />

1<br />

i<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

i<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

i<br />

1<br />

i<br />

i<br />

i<br />

1<br />

i<br />

1<br />

i<br />

i<br />

1<br />

i<br />

1<br />

i<br />

−<br />

−<br />

+<br />

−<br />

−<br />

−<br />

+<br />

−<br />

−<br />

−<br />

+<br />

−<br />

=<br />

−<br />

−<br />

+<br />

−<br />

−<br />

+<br />

−<br />

−<br />

=<br />

+<br />

−<br />

+<br />

+<br />

+<br />

−<br />

+<br />

+<br />

−<br />

−<br />

−<br />

+<br />

+<br />

−<br />

+<br />

+<br />

+<br />

−<br />

+<br />

−<br />

−<br />

−<br />

sehingga:<br />

)<br />

x<br />

(x<br />

)<br />

f(x<br />

x<br />

x<br />

x<br />

x<br />

)<br />

f(x<br />

x<br />

x<br />

1<br />

x<br />

x<br />

1<br />

)<br />

x<br />

(x<br />

)<br />

f(x<br />

x<br />

x<br />

x<br />

x<br />

)<br />

(x<br />

f'<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

-<br />

i<br />

i<br />

i<br />

1<br />

i<br />

i<br />

1<br />

i<br />

i<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

1<br />

i<br />

i<br />

i<br />

−<br />

⎟<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎜<br />

⎝<br />

⎛<br />

−<br />

−<br />

+<br />

⎟<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎜<br />

⎝<br />

⎛<br />

−<br />

+<br />

−<br />

+<br />

−<br />

⎟<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎜<br />

⎝<br />

⎛<br />

−<br />

−<br />

≅<br />

+<br />

+<br />

−<br />

+<br />

−<br />

+<br />

−<br />

−<br />

+<br />

−<br />

+<br />

71

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