Numerical Analysis

School : BEIHANG UNIVERSITY (BUAA)

Name : NGUYEN QUANG TUAN

Student ID : LS1413202

NUMERICAL ANALYSIS

Homework-2014/11/6

Problem 5.1 (b) Find [pic 1], [pic 2] and [pic 3] for [pic 4], the least square straight line for the data shown in following table.

Solution:

The system of equation for the least square is                                           [pic 5]                

[pic 6]

Numerical application, we will get

[pic 7]

[pic 8]

[pic 9]

The equation of straight line : [pic 10]

Now the corresponding square error will become as follows

[pic 11]

[pic 12]

Problem 5.5

To determine the best guess function we plot the points:

P1(1,2.3) , P2(2,6.1) , P3(3,10.7) , P4(4,16) , P5(5,21.9) , P6(6,28.3)

[pic 13]

Using the  graph above  and comparison with figure 5.2-1 the best guess function is ;

[pic 14]

Part a:

To linearize for g(x) = αeβx  , Xk = xk and Yk = In yk  so the transformed points are

P1(1,0.8329) , P2(2,1.8082) , P3(3,2.3702) , P4(4,2.7726) , P5(5,3.0865) , P6(6,3.3429).

[pic 15]

M = 6[pic 16][pic 17];  [pic 18][pic 19] [pic 20][pic 21];    [pic 22][pic 23] 2 = 441 ;  [pic 24][pic 25]