The equation x + ax +b = 0, has two real roots a and B. Show that the iteration method (1) X+1 =- (ax, + b)/x, is convergent near x = a, if | a| >[BI. (ii) Xt =- b/(x + a), is convergent near x = a, if | a|<|B |-

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The equation x? + ax + b = 0, has two real roots a and ß. Show that the iteration method
(i) Xk+1 =- (axx + b)/xk, is convergent near x = a, if | a | >| B|.
(ii) Xh+1 = - b/(x + a), is convergent near x = a, if | a|<|B |.
Transcribed Image Text:The equation x? + ax + b = 0, has two real roots a and ß. Show that the iteration method (i) Xk+1 =- (axx + b)/xk, is convergent near x = a, if | a | >| B|. (ii) Xh+1 = - b/(x + a), is convergent near x = a, if | a|<|B |.
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