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 per±orming the iteration. 6. Solve Exercise 1–3 by Newton’s 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 Olver’s Method , in honor o± the author’s ±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± Newton’s Method. 1 c ° 2006 Peter J. Olver...
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- Fall '09
- Numerical Analysis, decimal places, Peter J. Olver