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Decomposição de Cholesky

Decomposição de Cholesky

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Exercício A<br />

Fazendo L T x = y,<br />

⎡<br />

⎢<br />

⎣<br />

2 0 0 0<br />

− 2 1 0 0<br />

1 − 5 4 0<br />

4 − 2 1 5<br />

⎤ ⎡<br />

⎥ ⎢<br />

⎥ ⎢<br />

⎦ ⎣<br />

0<br />

0<br />

0, 25<br />

y4<br />

⎤<br />

⎥<br />

⎦ =<br />

⎡<br />

⎢<br />

⎣<br />

0<br />

0<br />

1<br />

0<br />

⎤<br />

⎥<br />

⎦ .<br />

Soluções do sistema triangular inferior obtidas pelas substituições<br />

sucessivas:<br />

y1 = 0<br />

y2 = 0<br />

y3 = 0, 25<br />

Manaíra Lima e Loïc Cerf<br />

<br />

<strong>Decomposição</strong> <strong>de</strong> <strong>Cholesky</strong><br />

5 / 11

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