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QRdecomposição
QRGram<-function(A){ #Processo de ortogonaliza��o de Gram-Schmidt n=length(A[1,]); m=length(A[,1]) V=A; Q=0*A; R=matrix(0,n,n) for (i in 1:n){ R[i,i]=sqrt(V[,i]%*%V[,i]); Q[,i]=V[,i]/R[i,i] for (j in (i+1):n){ if (j!=(n+1)){ R[i,j]=Q[,i]%*%V[,j]; V[,j]=V[,j]-R[i,j]*Q[,i]}}} QR <- new.env(); QR$Q <- Q; QR$R <- R as.list(QR) } c=c(1, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 1, 1, 2, 0, 3, 2, 1, 2, 1, 2, 1, 2, 3, 1, 27,23,31,31,22) A=matrix(c,5,6) A QRGram(A) TSup<-function(B,b){ n=length(B[,1]) x=0*b x[n]= b[n]/B[n,n] for (j in 1:(n-1)){ x[n-j]= b[n-j] for ( i in j:1){ x[n-j]= x[n-j]-B[n-j,n-j+i]*x[n-j+i] } x[n-j]= x[n-j]/B[n-j,n-j] } x }
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