Statistics and Numerical Methods: Unit III: Solution of Equations and Eigenvalue Problems
Short Questions and Answers
Fixed point Iteration x = g(x) method
Statistics and Numerical Methods : Unit - III : Solution of Equations and Eigenvalue Problems : Short Questions and Answers
SHORT QUESTIONS AND ANSWERS
1.
What is the condition for applying the fixed point iteration method (successive
approximation method) to find the real root of the equation x = f(x). [A.U CBT
M/J 2010] [A.U M/J 2016 R13] [A.U A/M 2017 R081A.U A/M 2018 R08]
Solution:
The condition for convergence is that in the neighbourhood of the root g'(x)
< 1
2.
What is the order of convergence for fixed point iteration ? [A.U N/D 2013]
Solution:
The convergence is linear and the convergence is of order 1.
3.
True or false : 'Iteration method' is a self correction method.
Solution:
True, in general, iteration method is a self correction method, since the
round-off error is smaller.
4.
In the case of fixed point iteration method, the convergence is
(a)
Linear, (b) Quadratic, (c) Very slow, (d) h2
Solution:
(a)
Linear.8
5.
If g (x) is continuous in [a, b], then under what condition of the iterative
method x = g(x) has a unique solution in [ a, b ]?
Solution:
The condition for convergence is that in the neighbourhood of the root g'(x)
< 1
6.
Write sufficient condition for convergence of an iterative method for f(x)=0
written as x= g(x) [A.U. A/M 2010, CBT N/D 2010] [A.U N/D 2016 R8-10]
Solution:
The
sufficient condition for convergence is g'(x) < 1
Statistics and Numerical Methods: Unit III: Solution of Equations and Eigenvalue Problems : Tag: : Fixed point Iteration x = g(x) method - Short Questions and Answers
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Related Subjects
Statistics and Numerical Methods
MA3251 2nd Semester 2021 Regulation M2 Engineering Mathematics 2 | 2nd Semester Common to all Dept 2021 Regulation