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Introduction to Linear Optimization and Extensions with MATLAB®
book

Introduction to Linear Optimization and Extensions with MATLAB®

by Roy H. Kwon
September 2013
Intermediate to advanced content levelIntermediate to advanced
362 pages
8h 44m
English
CRC Press
Content preview from Introduction to Linear Optimization and Extensions with MATLAB®
222 Introduction to Linear Optimization and Extensions with MATLAB
R
Go to Step 2.
Step 2: x
(2)
= x
(1)
+ (1)d
(1)
=
3/2
1/2
1
+ (1)
1/4
1/4
0
=
5/4
3/4
1
.
Table 6.1 shows the first 6 of the first 20 iterates of the Newton-Raphson
method. It should be noted that the error between successive iterates, i.e.,
x
(k+1)
x
(k)
is reduced by half, each iteration, which results in rapid con-
vergence toward the root x
=
1 1 1
.
Table 6.1 First 20 Newton-Raphson iterates for Example 6.1
k x
(k)
1
x
(k)
2
x
(k)
3
d
(k)
1
d
(k)
2
d
(k)
3
x
(k+1)
x
(k)
0 1 0 1 0.5 0.5 0 0.707107
1 1.5 0.5 1 0.25 0.25 0 0.353553
2 1.25 0.75 1 0.125 0.125 0 0.176777
3 1.125 0.875 1 0.0625 0.0625 0
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Publisher Resources

ISBN: 9781439862636