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Unformatted text preview: proximate the Fxed point, starting with p = 1 ? 3. (a) Write down Newton’s iteration as applied to the function f ( x ) = x 32. Simplify the formula as much as possible. (b) Write down the Secant iteration as applied to the same function f ( x ) = x 32. 4. (a) Construct the Lagrange polynomial interpolating the points x = 0 and x 1 = h , to approximate the function f ( x ) = cos x , where h > 0 is a small parameter. (b) Write down the error formula as applied to the above interpolation. Find an upper bound for the error on the interval [0 , h ], function of the parameter h . (c) Construct the Lagrange polynomial interpolating the points x = 0, x 1 = h , and x 2 = 2 h to approximate the function f ( x ) = cos x ....
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 Spring '08
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 Math, ObjectOriented Programming, Numerical Analysis, #, Bisection Method, UCLA MATH 151A/3

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