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{PARA 201 "" 0 "" {TEXT 203 70 "                Orthogonal Polynomials
 and Least Squares Approximation" }{TEXT 204 0 "" }}{PARA 201 "" 0 "" 
{TEXT 204 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 205 67 "        f(x) \+
approx.    a_0*phi_0(x) + a_1*phi_1(x) + a_2*phi_2(x);" }{TEXT 204 0 "
" }}{PARA 201 "" 0 "" {TEXT 204 0 "" }}}{EXCHG {PARA 201 "" 0 "" 
{TEXT 204 8 "        " }{TEXT 205 48 "First, we will try with a polyno
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{PARA 202 "" 1 "" {XPPMATH 20 "6#>I'alpha1G6\"$\"+nmmmm!#5" }{TEXT 
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t(x*sin(Pi*x),x=-1..1))/alpha1;" }{MPLTEXT 1 202 0 "" }}{PARA 202 "" 
1 "" {XPPMATH 20 "6#>I#a1G6\"$\"+$e'H\\&*!#5" }{TEXT 207 0 "" }}}
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205 63 "                Now, we will try with a polynomial degree thre
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200 "> " 0 "" {MPLTEXT 1 206 51 "a2:=evalf(int((x^2-1/3)*sin(Pi*x),x=-
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{MPLTEXT 1 206 37 "alpha3:=int((x^3-(3/5)*x)^2,x=-1..1);" }{MPLTEXT 1 
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