The equation x² + ax + b = 0, has two real roots a and ß. Show that the iteration method (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 ß. Show that the iteration method (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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![7. The equation x? + ax + b = 0, has two real roots a and B. Show that the iteration
method
(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 |.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8a7bff5-9fd3-472a-a291-20ed0c0761ca%2F3fb69e78-ffaf-4213-8264-df408e9948b3%2Fcbltllk_processed.png&w=3840&q=75)
Transcribed Image Text:7. The equation x? + ax + b = 0, has two real roots a and B. Show that the iteration
method
(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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