Orthogonal least square, parameterize unit vector using trigs (green)
Peitke see kaust õpilaste eest.
37
Orthogonal least square, unit vector constraint using Lagrange multiplier (green)
Peitke see kaust õpilaste eest.
46
k = a/b-b/a, solve quadratic equation
47
Avaldis 48: "m" Subscript, "l" , Baseline equals "N" left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket "Y" left bracket, "i" , right bracket , right parenthesis minus left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket , right parenthesis left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "Y" left bracket, "i" , right bracket , right parenthesisml=NN∑i=1XiYi−N∑i=1XiN∑i=1Yi
equals=
718.9 0 7 8 1 9 0 1 4718.907819014
48
Avaldis 49: "k" Subscript, "l" , Baseline equals StartFraction, 1 Over "m" Subscript, "l" , Baseline , EndFraction left parenthesis, "N" left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket squared , right parenthesis minus "N" left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "Y" left bracket, "i" , right bracket squared , right parenthesis plus left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "Y" left bracket, "i" , right bracket , right parenthesis squared minus left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket , right parenthesis squared , right parenthesiskl=1mlNN∑i=1Xi2−NN∑i=1Yi2+N∑i=1Yi2−N∑i=1Xi2
equals=
negative 3.6 3 7 3 4 9 4 4 0 9 4−3.63734944094
49
Avaldis 50: "a" Subscript, "l" , Baseline equals "k" Subscript, "l" , Baseline minus signum left parenthesis, "m" Subscript, "l" , Baseline , right parenthesis times StartRoot, "k" squared plus 4 , EndRootal=kl−signml·k2l+4
equals=
negative 7.7 8 8 2 9 0 4 1 3 2 5−7.78829041325
50
Avaldis 51: "b" Subscript, "l" , Baseline equals 2 times 10 to the 0 powerbl=2·100
equals=
22
51
Avaldis 52: "c" Subscript, "l" , Baseline equals negative StartFraction, 1 Over "N" , EndFraction left parenthesis, "a" Subscript, "l" , Baseline left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "X" left bracket, "i" , right bracket , right parenthesis plus "b" Subscript, "l" , Baseline left parenthesis, Start sum from "i" equals 1 to "N" , end sum, "Y" left bracket, "i" , right bracket , right parenthesis , right parenthesiscl=−1NalN∑i=1Xi+blN∑i=1Yi
equals=
3.2 0 4 8 0 0 6 9 3 1 93.20480069319
52
Avaldis 53: "a" Subscript, "l" , Baseline "x" plus "b" Subscript, "l" , Baseline "y" plus "c" Subscript, "l" , Baseline equals 0alx+bly+cl=0