# gqtest.jl -- Test 4-point Gaussian Quadrature bs=[2,0,2/3,0] xs=[-0.339981043584856,0.339981043584856,-0.861136311594053,0.861136311594053] V=xs' .^ [0:3;] ws=V\bs p(x)=x^2 - 3*x + 4 quad4=ws'*p.(xs) exact=26/3 println("p(x)=x^2 - 3*x + 4") println(" quad4=$(quad4)") println(" exact=$(exact)\n") p3(x)=5*x^3 - 2*x^2 + x - 16 quad4=ws'*p3.(xs) exact=-100/3 println("p3(x)=5*x^3 - 2*x^2 + x - 16") println(" quad4=$(quad4)") println(" exact=$(exact)\n") p7(x)=x^7 - 5*x^6 + x^4 - 2*x^3 + 2 quad4=ws'*p7.(xs) exact=104/35 println("p7(x)=x^7 - 5*x^6 + x^4 - 2*x^3 + 2") println(" quad4=$(quad4)") println(" exact=$(exact)\n") p8(x)=2*x^8 - x^7 + 13*x^4 quad4=ws'*p8.(xs) exact=254/45 println("p8(x)=2*x^8 - x^7 + 13*x^4") println(" quad4=$(quad4)") println(" exact=$(exact)\n") pt(x)=1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 quad4=ws'*pt.(xs) exact=425457/181440 println("pt(x)=1 + x + 1/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 + 1/720*x^6 + 1/5040*x^7 + 1/40320*x^8") println(" quad4=$(quad4)") println(" exact=$(exact)\n") quad4=ws'*exp.(xs) exact=exp(1)-exp(-1) println("exp(x)") println(" quad4=$(quad4)") println(" exact=$(exact)\n")