Differential Equations Solutions 139

# Differential Equations Solutions 139 - t so that f t = 0...

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149 CHALLENGE 24.5. Using the Lagrange form of the interpolating polynomial, we can write p ( f )= L 1 ( f ) t 1 + L 2 ( f ) t 2 + L 3 ( f ) t 3 , where L 1 ( f )= ( f f 2 )( f f 3 ) ( f 1 f 2 )( f 1 f 3 ) , L 2 ( f )= ( f f 1 )( f f 3 ) ( f 2 f 1 )( f 2 f 3 ) , L 3 ( f )= ( f f 1 )( f f 2 ) ( f 3 f 1 )( f 3 f 2 ) . It is easy to verify that L j ( f j )=1and L j ( f k )=0if j ± = k . Therefore, p ( f 1 )= t 1 , p ( f 2 )= t 2 ,and p ( f 3 )= t 3 , as desired. Now, we want to estimate the value of
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Unformatted text preview: t so that f ( t ) = 0, and we take this estimate to be p (0). We calculate: L(1) = f(2)*f(3)/((f(1)-f(2))*(f(1)-f(3))); L(2) = f(1)*f(3)/((f(2)-f(1))*(f(2)-f(3))); L(3) = f(1)*f(2)/((f(3)-f(1))*(f(3)-f(2))); testimated = L*t;...
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