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fi Two Mark Questions and Answers iterative method. -. whi 1. Define convergence of an it ae Solution: ™ | iy? iterative method we find a sequence { xk = of approximations to the C Using an | = 0, where a is the exact root, then the method is Said Di —a le lim |v, — @ of f (x) = 0. If lim fa be convergent. 2. What are the criteria used to terminate an iterative procedure? Solution: — - I i" : ft ’ — 4. a t ’ _ eee ee ee Se ee oe ee, i : ; : y + |! ry #7 1 eT er AS 2 Bo = a (fo . naw ae > ao, 7. FS r«¢ rT se > \ k, = Let € be the prescribed error of tolerance. Then the rec — ae = a 3 wa = i a 4 it = —, 4 X a. 4 a a ad F vc. a i. et a : al es 1 aaa = - = i] A, 1 1 - in - " } oa Be 1 aT I a 4 4 Th. : \ = = me ae ’ I i a fi) ff fo £ 5 } i) j 4 4 w Mt lly het in mi ci oe wit <. ai wf J Lr jo i ee, YY Sf —e es ~ Ae wm es hd Pa | = q a , . . = © ”’} - a) 7 | Systenis of Linear Equations 1S There are direct methods for finding all the roots of cubic and fourth degree polyno t these methods are diff se erat 2 me nny difficult to use. However, direct methods for finding rors ee 7 nts z vis of degree greater than 4 and transcendental equations aren ature. In iterative methods we can solve such equations also. 4. Give two direct methods to solve a system of linear equations. i) Gauss elimination method ii) Gauss- Jordan method. 12 8° 7 eho Ue oie) 15 1 4/5 |3 (5 23/5 a Hz > Ro — 3Ry 4 23 15 > t+ -y=3and —y= — — =Y Ry Sy 4 415 57 — £=3--.— = — 5°93 «(2 - Bs 2 oe __ 6, What are the advantages of a direct method for solving a linear system of algebraic a equation AX = B? 1 ate 's Jills a ct met thod produces the solution in a finite number of steps. The number of oper- count can be calculated. rect methods we use for ing the system of equations AX = B? } the inverse of a square matrix? x ion met! od and Gauss-Jordan method Oe ee Pes oe Scanned with CamScanner 
