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Chapter 7

Exercise Set 7.1

2.

(a)

Since with equality if and only if for all i, properties (i) and (ii) in Definition 7.1 hold.

Also,

so property (iii) holds.

Finally,

so property (iv) holds.

4.

(c) 4 (d) 12

6.

(c) 4 (d) 12

10.

Using the Cauchy-Buniakowsky-Schwarz (CBS) inequality gives

Thus,

Exercise Set 7.3

1.

(f)

The kth iterates of the Jacobi method are

The first two iterates are

2.

(f)

The kth iterates of the Gauss-Seidel method are

The first two iterates are

6.

(f)

The kth iterates of the SOR method are:

With and the first two iterates are:



Michael Lunney
Thu Oct 17 18:23:51 PDT 1996