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Unformatted text preview: What is the rate o convergence? ( c ) Predict how may iterates will be needed to get the fxed point accurate to 4 decimal places starting with the initial guess u (0) = 1. ( d ) Check your prediction by perorming the iteration. 6. Solve Exercise 13 by Newtons Method. 7. ( a ) Let u ? be a simple root o f ( u ) = 0. Discuss the rate o convergence o the iterative method (sometimes known as Olvers Method , in honor o the authors ather) based on g ( u ) = u + f ( u ) 2 f 00 ( u )2 f ( u ) f ( u ) 2 2 f ( u ) 3 to u ? . ( b ) Try this method on the equation in Exercise 3, and compare the speed o convergence with that o Newtons Method. 1 c 2006 Peter J. Olver...
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 Fall '09
 Olver

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