QUIZ-7-Answer - x p + + + + = 1 1 1 ... ) ( . Set up a...

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QUIZ #7 ENGR 3723 Name:______________________________ Closed book- closed notes PROBLEM 1 Consider 2 . 27 3 6 . 13 2 7 . 7 1 1 . 2 0 i i y x A) (10 points) What degree is the polynomial that interpolates these data? ANSWER: 4 points 3 rd degree polynomial B) (50 points) Eliminate one point and obtain the corresponding interpolating polynomial using Newton’s method. ANSWER: We use 6 . 13 2 7 . 7 1 1 . 2 0 ) ( i i i x f y x = ) )( ( ) ( ) ( 1 0 2 0 1 0 2 x x x x b x x b b x f + + = 0 2 0 1 0 1 1 2 1 2 2 2 0 0 1 1 1 0 0 0 ) ( ) ( ) ( ) ( ) ( ) ( ) ( x x x x x f x f x x x f x f b x x x x x f x f b x x x f b x x = = = = = =
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C) (40 points) Propose a polynomial as follows: n n n n a x a x a x a x p + + + + = 1 1 1 0 ... ) ( . Use three points to substitute directly: n i n n i n i i a x a x a x a
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Unformatted text preview: x p + + + + = 1 1 1 ... ) ( . Set up a linear system to obtain the coefficients a i directly. ANSWER: We use the same points as in 1 . 2 2 4 2 4 6 . 13 1 . 2 7 . 7 1 . 2 ) ( 1 2 1 2 2 1 2 2 2 1 2 1 2 1 1 2 1 1 2 2 1 2 2 1 2 + + = + + = + + = = + + = + + = + + = = = + + = = + + = a a a a a a x a x a y a a a a a a x a x a y a a x a x a y a x a x a x p This system can be solved for a and 1 a...
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This note was uploaded on 08/31/2011 for the course ENGR 3723 taught by Professor Staff during the Summer '11 term at Oklahoma State.

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QUIZ-7-Answer - x p + + + + = 1 1 1 ... ) ( . Set up a...

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