Numerical Analysis
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School : BEIHANG UNIVERSITY (BUAA)Name : NGUYEN QUANG TUAN Student ID : LS1413202NUMERICAL ANALYSISHomework-2014/11/6Problem 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.x1.01.21.41.61.8y-5-3-203Solution: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 areP1(1,0.8329) , P2(2,1.8082) , P3(3,2.3702) , P4(4,2.7726) , P5(5,3.0865) , P6(6,3.3429).x123456y0.83291.80822.37022.77263.08653.3429[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]