Use Theorem 10.6 to show that G ; D C E 3 E 3 has a unique fixed point in D. Apply

Chapter 10, Problem 5

(choose chapter or problem)

Use Theorem 10.6 to show that G ; D C E 3 E 3 has a unique fixed point in D. Apply fixed-point iteration to approximate the solution to within 10~5 , using the norm. a. G: v..A., -ra. r 00 "^-'-"-5 vr.o.,::5 .0.0.,. 1 -.u. IOJT - 3\' 20 ^ 60 D = ((xl ,X2,x3)' I -1 < X; < 1, / = 1, 2, 3 ) , , / 13 - x| + 4X3 11 + X3 - xf 22-hx3 b. Gixi, X2, xi) = . , V 1 2 3 ' V 15 10 25 D = {(X|,X2,X3)' | 0 < x, < 1.5,/ = 1,2, 3) C. G{X|, X2, X3) = (1 C0S(XiX2X3), 1 (I X])'^4 O.OSx2 + 0.15X3, X 2 + 0.Ix| -0.01X2+ 1)': D = {(xi, X2, X3)' | 0.1 < X| <0.1, 0.1 < X2 < 0.3, 0.5 < X3 < 1.1 } d. G(xi,X2,x3)= Qcos(x2X3)+ ^^^/x2 + sin x3 + 1.06 0.1, I ..... 1077-3 20 60 D = {(XI.xz.XJ)' | -1 < Xi < I,/ = 1,2,3}