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Unformatted text preview: [4 , 6] . Table: Approximation p n and absolute error  p np  versus iteration number n in Bisection method 1 n p n  p np  5.0000000 0.0828141 1 4.5000000 0.4171859 2 4.7500000 0.1671859 3 4.8750000 0.0421859 4 4.9375000 0.0203141 5 4.9062500 0.0109359 6 4.9218750 0.0046891 2. (Order of Convergence) Apply the theorems on pp. 9091 to the following problems: (a) Section 2.3 #8 g ( √ a ) = √ a . The conditions of the theorem on page 91 hold. g Í ( √ a ) = 0 but g Í ( √ a ) Ó = 0, so α = 2 and the asymptotic error constant is 1 / 2 √ a . (b) Section 2.3 #9 g ( √ a ) = √ a . The conditions of the theorem on page 91 hold. g Í ( √ a ) = g Í ( √ a ) = 0, but g Í ( √ a ) Ó = 0. Thus α = 3 and the asymptotic error constant is 1 / 4 a . 2...
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 Fall '08
 KRASNY
 Calculus, matlab, Optimization, Mathematical analysis, Logarithm

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