kindly help and guide me how i can correct this code, my target is to find
x1,x2,x3 but when the matrix is positive definite i do get
the solution correctly as you can see from the code but when the matrix is
indefinite we dont get the solution . i want know how i can correct this
problem if there is any method that can correct it thanks
#Q<-matrix(c(0.2,0.5,.05,0.1),2,2)#####Indefinite
#b<-rbind(0.1,0.2)
Q<-matrix(c(2.97,-2.47,-2.47,3.97),2,2)###positive definite
b<-rbind(-1.99,0.99)
#Q<-matrix(c(5,-3,-3,2),2,2)
#b<-rbind(0,1)
H0<-diag(2)
x0<-rbind(0,0)
d0<-b
g0<--b
a0<--(t(g0)%*%d0)/(t(d0)%*%Q%*%d0)
x1<-x0+a0[,1]*d0
dx0<-x1-x0
g1<-Q%*%x1-b
dg0<-g1-g0
exp0<-t(dg0)%*%dx0
exp1<-(1+((t(dg0)%*%H0%*%dg0)/(exp0[,1])))####first step result
exp2<-t(dx0)%*%dg0
exp3<-(exp1[,1]*(dx0%*%t(dx0)))/exp2[,1]########second step result
exp4<-t(dg0)%*%dx0
exp5<-(dx0%*%t(dg0)%*%H0+H0%*%dg0%*%t(dx0))/exp4[,1]#######third step
H1<-H0+exp3-exp5
d1<--H1%*%g1
a2<--(t(g1)%*%d1)/(t(d1)%*%Q%*%d1)
x2<-x1+a2[,1]*d1
g2<-Q%*%x2-b
dg1<-g2-g1
dx1<-x2-x1
exp6<-t(dg1)%*%dx1
exp7<-(1+((t(dg1)%*%H1%*%dg1)/(exp6[,1])))####first step result
exp8<-t(dx1)%*%dg1
exp9<-(exp7[,1]*(dx1%*%t(dx1)))/exp8[,1]########second step result
exp10<-t(dg1)%*%dx1
exp11<-(dx1%*%t(dg1)%*%H1+H1%*%dg1%*%t(dx1))/exp10[,1]#######third step
H2<-H1+exp9-exp11
d2<--H2%*%g2
a3<--(t(g2)%*%d2)/(t(d2)%*%Q%*%d2)
x3<-x2+a3[,1]*d2
g3<-Q%*%x3-b
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