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chapter1 - i book 2005/4/7 22:31 page S-1#22 i i i Answers...

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“book” — 2005/4/7 — 22:31 — page S-1 — #22 Answers to Selected Exercises for Chapter 1 Section 1.1 (page 16) 1. ¯ x = 1 . 4, s = 2 . 880972 3. 5 2 . 236067977 5. GIVEN: the integers n , m and p the elements in the matrix A , a ij the elements in the matrix B , b jk STEP 1: for i from 1 to n STEP 2: for k from 1 to p STEP 3: initialize sum to 0 STEP 4: for j from 1 to m add a ij b jk to sum end STEP 5: set c ik = sum end end OUTPUT: the elements in the matrix C , c ik 7. (a) GIVEN: non-zero real number a starting approximation x 0 convergence parameter maximum number of iterations Nmax STEP 1: for iter from 1 to Nmax STEP 2: compute x 1 = x 0 (2 ax 0 ) STEP 3: if | x 1 x 0 | < , OUTPUT x 1 STEP 4: copy the value of x 1 to x 0 end OUTPUT: “maximum number of iterations has been exceeded” (b) 1 / 37 0 . 027027016 9. (b) x · y = 3 11. (b) 2 1 dx/x 0 . 691219891 15. (a) GIVEN: convergence parameter maximum number of terms Nmax STEP 1: initialize sum to 4 and sign to -1 STEP 2: for i from 1 to Nmax STEP 3: set term = 4 / (2 i + 1) S-1
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“book” — 2005/4/7 — 22:31 — page S-2 — #23
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