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numerical analysis for problem 3 the interval is 112...

Question: numerical analysis for problem 3 the interval is 112...

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Numerical analysis

For problem 3 the interval is ( 1.1,2)

- MAT-362 (1191-1778) INTRO TO Problem 1 Use the fixed-point iteration theorem to show that gx) 2-* has a unique fixed point on [1,1]. Hint: olra-z-a-ina. Problem 2 Consider three functions: 23, 192(z) =v 2r+3, g3(z),32 9:(z) = and (a) Show that fixed points of each g(x) are roots of f(x) 2-3. (b) Which g() has a unique fixed point in [1, 4] guaranteed by the Fixed Point Theorem? Problem 3 Use the fixed point iteration to find the solution of e-3a on [1,2] with zo = 1.5 correct to roughly within 10-3. Hint: Use the correct g(r) for f(z) = ez-3a. Problem 4 Find n for which the nth iteration by the Fixed-point method guarantees to a the root of f(x) -coS on 0, ] with accuracy within 10- using o

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