Simon Fraser MACM 316 Midterm Questions
Simon Fraser College MACM 316 - Numerical AnalysisSpring time period 2013Drawback: Contemplate the next equationf (x) = x ? 2?xRecall that:di) (a?x) = a?x ln a ii) ln 2 zero.693147dx1. 2 ptsHow many (actual) options does the unique equation f (x) = zero have? Clarify.2. 2 ptGiven a root-finding downside f (p) = zero, outline an preliminary interval [a, b] with a view to apply theBisection methodology.three. three ptsDetermine the variety of iterations essential to discover a answer correct to inside 10?7 utilizing the Bisection methodology on the interval outlined in (2), i.e. | p ? pn | ? 10?7.Apply three consecutive iterations of the Bisection methodology on the interval outlined in (2) utilizing three-digit rounding arithmetic.5. three ptsApply Newton’s methodology to get better | f (pn ) | < zero.005. Use four-digit chopping arithmetic.Change the unique equation to a fixed-point type x = g(x) and outline the sequence pn+1 = g(pn ).Resolution :A hard and fast-point type is7. three ptsTwo fixed-point varieties g1(x) and g2(x) have been outlined. Which of those varieties displays extra fast convergence, if g0 (x) ? zero.15 and g0 (x) ? zero.87 close to the mounted level?1 28. 2 ptsWhat ought to one count on when utilizing the Secant methodology on a 32-bit structure, and beginning with the 2 preliminary approximations p0 = (9A27)16 and p1 = (FECA)16 ?bonus. 2 ptsDetermine the second Taylor polynomial for f (x) about x0 = zero. ApproximateZ zero.4using P2(x).f (x) dx0