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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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 |.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.5: Iterative Methods For Solving Linear Systems

Problem 21EQ

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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 |.

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