MACM 316 Study Guide - Final Guide: Round-Off Error, Bijection
9 Jan 2019
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Suppose that an iterative root- nding method produces a sequence of approximations pn that has order 3 convergence to the exact solution p0 with asyptotic error constant 0. 4. If the absolute error of the rst approximation p0 is 0. 7, estimate the number of iterations that are necessary to achieve accuracy 10 9. (hints: given limn p|3 0. 41+3|pn 2 p|32 which id 0. 7. ) (ans: n 3) Find one root of the equation using the bijection method. How many iterations are needed to reduce xtol to less than 0. 1: similar to the previous question. Find lagrange interpolating polynomial of degree 3 and use it to compute the approximation of cos(2. 1): consider the polynomial x5 6x4 + 8x3 + 8x2 + 4x 40. Starting with p0 = 3, perform two iterations of newton-raphson methods to nd a root of the polynomial: let f(x) = sinx. (a) calculate aaproximations to f (0. 8) using the formula f (x) =
