Handout22 - COMPUTER SCIENCE 349A Handout Number 22...

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1 COMPUTER SCIENCE 349A Handout Number 22 EXAMPLES: LAGRANGE INTERPOLATING POLYNOMIAL 1. The case n = 1 is called linear interpolation, and consists of constructing a straight line through 2 points () ( ) ) ( , ) , ( and ) ( , ) , ( 1 1 1 1 0 0 0 0 x f x y x x f x y x = = . 0 1 0 1 1 0 1 0 ) ( and ) ( x x x x x L x x x x x L = = and thus ) ( ) ( ) ( 1 0 1 0 0 1 0 1 x f x x x x x f x x x x x P + = . Note that P ( x ) is clearly a linear (first order) polynomial in the variable x , and that ) ( ) ( and ) ( ) ( 1 1 0 0 x f x P x f x P = = , which verifies that P ( x ) is the desired interpolating polynomial. 2. A complete elliptic integral is defined by = 2 / 0 2 2 sin 1 ) ( π z k dz k K . The following values can be obtained from numerical tables: sin 1 kK ( k ) 65 o 2.3088 66 o 2.3439 67 o 2.3809 Construct the quadratic (order
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Handout22 - COMPUTER SCIENCE 349A Handout Number 22...

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