Question

1.6.1. Consider the ill-conditioned system of Example 1.6.1: 835x667y 168, .333.x266y = .067. (a) Describe the outcome when you attempt to solve the system using 5-digit arithmetic with no (b) Again using 5-digit arithmetic, first row scale the system before attempting to solve it. Describe to what extent this helps (c) with the exact solution (d) Using 6-digit arithmetic, compute the residuals for your solution of part (c), and interpret the results. (e) For the same residuals, but use results (f) Formulate a concluding statement that summarizes the points made in parts (a)-(e) scaling Now use 6-digit arithmetic with no scaling. Compare the results solution obtained in part (c), again compute the 7-digit arithmetic this time, and interpret the

Answer 1

Consider te ) onditioned system 0835 21 t0.667y0.168 0:333 X+ 0.266_y Matrix Prom s. 01067 168 8.35 667 266 333 a) Describe th outcoe wheh you attempt to solve Phe systcm using 5-dgit_arthtic ih ha scaling. 5-digit arithetic with $35 662 1333 scalng 68 ho tya By Applying Rr-835 Ri .333 R Fale3- 835 667 89F .0.0000 8.3.5 xt 667 y 0.168

XO68-0.667n .835 -0.79880 (b)Apin using s digit arthetic Pirst sclak the System before atterphing to solve it pescribe to what extent this helps 5 - digit aithmetic Pirst Scality in al) Yow Apely R 835 ala) 798 &0 266 .2oll9 067 :333 APPly Ri Ri 33 R t 2ol19

A12X220119. -O59761 835) (-as6)+0. 701639 O18

Axihticho scalihg the cract solutioh 2ONOU usc 6 Copare the resul 6-disit arhereti wih ho scaling 8 667 0.0000121 l 168-6679 O.835 1

Now using 6 digit arhctic onpute tae residuals fy your solution of Part Ciand inkepet the rsul FX0m Part digit arihtic h10 7

() Foraulate that subni2es Par H Ca)-(e) a corcluding statersen the Poins haade n tven it loMPuted nesiduals are o you cannot Sat You have heCact besure