Exam1 sol - MATH 4334 EXAM I — 1 F‘iTId'an equivalent...

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Unformatted text preview: MATH 4334 EXAM I — Oct 11, 2011 1. F‘iTId'an equivalent formula for the £0 your answer. 1+cos(w) forxzar 2. ( 2X ): ——L+ 1-5054; : H 1-677 4‘_ ' zfathxlzeftnwefi _ (-49% z 4 z 2 Hrva aqrrbfiéG—jm’fa‘ GWQ Z .— 511.r/%_fi.ze>2,<fi almi‘gl— If” _ 2. Discuss the propagation of error for the followingI if errors in p, q, r are 6p, eq, 6,, respectively. (a) The sum of three numbers 11 + q + T 2 @ + 6p) + (c? + 59) + (F + er). Please justify your answer. (13) The quotient of two numbers p/q = (35 + leg/(:7 + eq). Please justify your answer. A} P.) N If! 6:) W+$+rfliptfifiy)fi5\eyl eg'i'é') 6.69176? . GP h-G—%fl€% or iii? Whig-fir? ~~.—--~_ 2' if? Hung N 60 P g g 45- ‘ %\+KP)C"K3) I?" ’12 (Hfipm R1) 4 )QK 4%)”) “W W “379"” «ea-r 3. (a) Rewrite the following linea'ir system in a fixed point form, x = F(x), for which the fixed—point iteration is sure to converge for any initial guess x = [mmym zo]T. Please justify your answer. 31231:: a: +52=0 [email protected]fi Efi‘mzm” e; x21 J —%/ ._, x 1/”\i/’.f «C "We lg g 4 X: \i c.1é fiéfiw—E/V: '3ch 7=Z/—’9"% '9 z ’2 M a 9x :(1/ I " r 43"??? {a Ejfi/gd—j __'__7 ‘7 a gait/CO 5kg @ = FM ) W kid/0&0 :1?) 7] 73"} l u)+)a’fi_\:b+/é éflg l/iiri m be _ \ #1/41 m be eel—sewn. \Bfilvrlfil'l '02 Z 4 M 3'93 fiélzlfii’f’é l pelilgqlrlse 4. We-want to find DUN using the Newton-Raphson iteration method. Assume the givan constant D > 0 and N is a. positive integer. Write out the needed recursive formula that will give us an answer for ('7’... N _ ( r _ meéfl/g me-.—_x "’exw)..X._ 517%; 76/05?) ’17 NX a“ 4‘) 5. (a) Without finding A“, estimate the condition number for A using the uniform norm. Please justify 6111 1411 A=1151 1117 your answer. (in) Write amatiab code that does the same thingasyou did by hand in part (a). I. - i 60 AWMMW%R&“QE 0/617 8’: KR {‘1‘} W MinyW/gilo] :i9-—-— =SL'5 ‘ W"— : #757,???“ MUfiHB / inn“ 0 3 a Q - a o ‘1‘” ' , 0 0 00 j ,' 5 1° m7 5 b) AJHW PM” U ) ifl‘ naivilil i116” ’) B i: J ) Cr: " o llfl mp" W * 6% (Mn 29%!» (Alma) +“g’mm’m/ dbm'mt-ih ’ ‘ 94, {m w» ’Dtn): 1))W(C(flla))¢6¢&CC[Wig r I , (CWI' ‘ ...
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Exam1 sol - MATH 4334 EXAM I — 1 F‘iTId'an equivalent...

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