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The equation x² + ax + b 0, has two real roots a and B. Show that the iteration (i) Xk+1 = - (axk + b)/xk, is convergent near x = a, if | a | > | ß |, (ii) Xk+1 = - b/(Xk + a), is convergent near x = a, if | a |< | ß |.

The equation x² + ax + b 0, has two real roots a and B. Show that the iteration (i) Xk+1 = - (axk + b)/xk, is convergent near x = a, if | a | > | ß |, (ii) Xk+1 = - b/(Xk + a), is convergent near x = a, if | a |< | ß |.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The equation x² + ax + b = 0, has two real roots a and ß. Show that the iteration me (i) Xk+1 = - (axk + b)/xk, is convergent near x = a, if | a | > | ß |, (ii) Xk+1 = – b/(xk + a), is convergent near x = a, if | a | < | B |.
Transcribed Image Text:The equation x² + ax + b = 0, has two real roots a and ß. Show that the iteration me (i) Xk+1 = - (axk + b)/xk, is convergent near x = a, if | a | > | ß |, (ii) Xk+1 = – b/(xk + a), is convergent near x = a, if | a | < | B |.
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