review2s - (4) T = -1 3-1 , c = 4 3 1 estimates are , 4 3 1...

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Numerical Analysis/Fall 2009/Review #2/Solutions (1) x y xy x 2 0 2 0 0 1 1 1 1 2 2 4 4 3 8 24 9 6 13 29 14 ± 4 6 13 6 14 29 ² y = 0 . 4 + 0 . 9 x. (2) (a) Z π - π sin mx cos nxdx = 1 2 Z π - π sin( m + n ) x + sin( m - n )) dx = - 1 2 ± cos( m + n ) x m + n + cos( m - n ) x m - n ² π - π = 0 since cos is an even function. (b) Since f is an even function, all the b k are zero. πa 0 = π (look at R π - π f ( x ) dx ). For k > 0 πa k = Z π - π f ( x ) cos kxdx = 2 Z π 0 x cos kxdx = 2 ± x sin kx k + cos kx k 2 ² π 0 = 2 k 2 (cos - 1) = 2 k 2 (( - 1) k - 1) . (3) Note that a b = ³ 1 3 3 2 ´ . F 4 ( a ) = ³ 3 i 1 - i ´ F 4 ( b ) = ³ 3 1 + 2 i - 1 1 - 2 i ´ F 4 ( a b ) = ³ 9 - 2 + i - 1 - 2 - i ´ F 4 ( a ) × F 4 ( b ) = ³ 9 - 2 + i - 1 - 2 - i ´
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Unformatted text preview: (4) T = -1 3-1 , c = 4 3 1 estimates are , 4 3 1 , 1-1 3 , 13 9 . (5) (a) 7 (b) 5 (6) The condition number of A is 4 . 0001 60001 240000, which is high. In this case, the residual being close to zero does not mean that the estimate is close to a solution....
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This note was uploaded on 10/10/2010 for the course MATH 01:640:111 taught by Professor Carey during the Spring '10 term at Saint Louis.

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review2s - (4) T = -1 3-1 , c = 4 3 1 estimates are , 4 3 1...

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