Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.6: Inequalities
Problem 80E
See similar textbooks
icon
Related questions
Question
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 |.
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
SEE MORE TEXTBOOKS