MATH 4650 Midterm: Math4650SampleExam1
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Sample exam i math 4/5650 - numerical analysis - fall 2017: problem 1. Show this analytically and geometrically (graph of g is included for convenience). (b) use the theoretical bound |xn x | kn. 1 k|x1 x0| (where k < 1 is an upper bound for |g (x)|, x i) to obtain a theoretical bound on the number of iterations needed to approximate the xed point to within. You may pick x0 = 3: problem 3. Using divide di erences, show that the polynomial interpolating the following data has degree three: x f (x) 1 + x (a) find the third degree taylor polynomial expanded about x0 = 0 and use it to approximate f (0. 1). Find a bound for the error in this approximation. What is the error estimate now? (c) write down (without computing the coe cients explicitly) the clamped cubic spline interpolation s(x) using the three points x0 = 0, x1 = 0. 5 and x2 = 1.
