Unformatted text preview: 21f [1]f [0] 12 = (81)(10) 2 = 3. 3.2.11. (a) Calculation shows P ( x ) = f ( x ) and Q ( x ) = f ( x ) for x =2 ,1 , , 1 , 2. (b) Both polynomials are equal (to x 33 x + 1), just written in a diﬀerent form. 3.3.1a. Construct a divideddiﬀerence table as follows. x = 8 . 3 f [ x ] = f (8 . 3) = 17 . 56492 f [ x ,z ] = f (8 . 3) = 3 . 116256 z = 8 . 3 f [ z ] = f (8 . 3) = 17 . 56492 . 0594800 f [ z ,x 1 ] = ······ = 3 . 134100. 002022222 x 1 = 8 . 6 f [ x 1 ] = f (8 . 6) = 18 . 50515 . 0588733 f [ x 1 ,z 1 ] = f (8 . 3) = 3 . 151762 z 1 = 8 . 6 f [ z 1 ] = f (8 . 6) = 18 . 50515 (See, e.g., Table 3.13 in the text.) The coeﬃcients for the Newton form of the approximating polynomial are on the top edge of this table: H ( x ) = 17 . 56492+3 . 116256( x8 . 3)+0 . 0594800( x8 . 3) 2. 002022222( x8 . 3) 2 ( x8 . 6). Date : Due Thursday 7/09. 1...
View
Full
Document
This note was uploaded on 04/06/2010 for the course MATH various taught by Professor Tao/analysis during the Spring '10 term at UCLA.
 Spring '10
 tao/analysis
 Math

Click to edit the document details