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 |.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 58E
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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 |.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86541e5a-f0d2-4912-a794-7f1ac87e8dfb%2F6fd95d2f-00e0-4e15-8ddd-4140668f044d%2Fnc5cpi_processed.jpeg&w=3840&q=75)
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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